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Subject: Lucas, can triangles help you understand hexagons?
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 Content preview:  More often than not, the art of solving complex geometry problems
    comes down to triangles. How do you split up figures into triangles, and
   how does that help you solve the problem? Brilliant ( https://brilliant.org/practice/triangles-and-hexagons-2/?problem=basic-2d-geometry-problem-163296&chapter=introduction-to-basic-2d-geometry&utm_source=brilliant&utm_medium=email&utm_campai
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--9a7cbc817c643cb43c4bd869b24f6cd6ff7f429aeaa6cfa159c2e1ec52ec
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More often than not, the art of solving complex geometry problems comes dow=
n to triangles. How do you split up figures into triangles, and how does th=
at help you solve the problem?

Brilliant ( https://brilliant.org/practice/triangles-and-hexagons-2/?proble=
m=3Dbasic-2d-geometry-problem-163296&chapter=3Dintroduction-to-basic-2d-geo=
metry&utm_source=3Dbrilliant&utm_medium=3Demail&utm_campaign=3Dnls-ap1-q&ut=
m_term=3Dgeo1-triandhex&auto_login_key=3Dm7WDZdTgVglYeON8BaRCy2bbtZ4PJPVrzT=
uO5kkaWu&utm_content=3Dbrilliantlogo )

Take a look at this regular hexagon, and try to see if there=E2=80=99s any =
relation to the blue and orange areas.
( https://brilliant.org/practice/triangles-and-hexagons-2/?problem=3Dbasic-=
2d-geometry-problem-163296&chapter=3Dintroduction-to-basic-2d-geometry&utm_=
source=3Dbrilliant&utm_medium=3Demail&utm_campaign=3Dnls-ap1-q&utm_term=3Dg=
eo1-triandhex&auto_login_key=3Dm7WDZdTgVglYeON8BaRCy2bbtZ4PJPVrzTuO5kkaWu&u=
tm_content=3DpaneTextLink )

picture or diagram ( https://brilliant.org/practice/triangles-and-hexagons-=
2/?problem=3Dbasic-2d-geometry-problem-163296&chapter=3Dintroduction-to-bas=
ic-2d-geometry&utm_source=3Dbrilliant&utm_medium=3Demail&utm_campaign=3Dnls=
-ap1-q&utm_term=3Dgeo1-triandhex&auto_login_key=3Dm7WDZdTgVglYeON8BaRCy2bbt=
Z4PJPVrzTuO5kkaWu&utm_content=3DimageLink )

More often than not, the art of solving complex geometry problems comes dow=
n to triangles. How do you split up figures into triangles, and how does th=
at help you solve the problem?
( https://brilliant.org/practice/triangles-and-hexagons-2/?problem=3Dbasic-=
2d-geometry-problem-163296&chapter=3Dintroduction-to-basic-2d-geometry&utm_=
source=3Dbrilliant&utm_medium=3Demail&utm_campaign=3Dnls-ap1-q&utm_term=3Dg=
eo1-triandhex&auto_login_key=3Dm7WDZdTgVglYeON8BaRCy2bbtZ4PJPVrzTuO5kkaWu&u=
tm_content=3DpaneTextLink )

picture or diagram ( https://brilliant.org/practice/triangles-and-hexagons-=
2/?problem=3Dbasic-2d-geometry-problem-163296&chapter=3Dintroduction-to-bas=
ic-2d-geometry&utm_source=3Dbrilliant&utm_medium=3Demail&utm_campaign=3Dnls=
-ap1-q&utm_term=3Dgeo1-triandhex&auto_login_key=3Dm7WDZdTgVglYeON8BaRCy2bbt=
Z4PJPVrzTuO5kkaWu&utm_content=3DimageLink )

In Triangles and Hexagons, you=E2=80=99ll learn how complex and beautiful g=
eometry problems can be thought of in terms of triangle pieces. Once you kn=
ow how to break down a problem, the solution will be that much easier to se=
e.

Where we start:
( https://brilliant.org/practice/triangles-and-hexagons-2/?problem=3Dbasic-=
2d-geometry-problem-163296&chapter=3Dintroduction-to-basic-2d-geometry&utm_=
source=3Dbrilliant&utm_medium=3Demail&utm_campaign=3Dnls-ap1-q&utm_term=3Dg=
eo1-triandhex&auto_login_key=3Dm7WDZdTgVglYeON8BaRCy2bbtZ4PJPVrzTuO5kkaWu&u=
tm_content=3DpaneTextLink )
picture or diagram ( https://brilliant.org/practice/triangles-and-hexagons-=
2/?problem=3Dbasic-2d-geometry-problem-163296&chapter=3Dintroduction-to-bas=
ic-2d-geometry&utm_source=3Dbrilliant&utm_medium=3Demail&utm_campaign=3Dnls=
-ap1-q&utm_term=3Dgeo1-triandhex&auto_login_key=3Dm7WDZdTgVglYeON8BaRCy2bbt=
Z4PJPVrzTuO5kkaWu&utm_content=3DimageLink )

The figure above is a regular hexagon split up into a triangle, a rhombus, =
and a trapezoid.

If the area of the blue triangle is 3, what is the area of the orange trape=
zoid?
( https://brilliant.org/practice/triangles-and-hexagons-2/?problem=3Dbasic-=
2d-geometry-problem-163296&chapter=3Dintroduction-to-basic-2d-geometry&utm_=
source=3Dbrilliant&utm_medium=3Demail&utm_campaign=3Dnls-ap1-q&utm_term=3Dg=
eo1-triandhex&auto_login_key=3Dm7WDZdTgVglYeON8BaRCy2bbtZ4PJPVrzTuO5kkaWu&u=
tm_content=3DpaneTextLink )

* 8 ( https://brilliant.org/practice/triangles-and-hexagons-2/?problem=3Dba=
sic-2d-geometry-problem-163296&chapter=3Dintroduction-to-basic-2d-geometry&=
utm_source=3Dbrilliant&utm_medium=3Demail&utm_campaign=3Dnls-ap1-q&utm_term=
=3Dgeo1-triandhex&auto_login_key=3Dm7WDZdTgVglYeON8BaRCy2bbtZ4PJPVrzTuO5kka=
Wu&utm_content=3Dchoice )
9 ( https://brilliant.org/practice/triangles-and-hexagons-2/?problem=3Dbasi=
c-2d-geometry-problem-163296&chapter=3Dintroduction-to-basic-2d-geometry&ut=
m_source=3Dbrilliant&utm_medium=3Demail&utm_campaign=3Dnls-ap1-q&utm_term=
=3Dgeo1-triandhex&auto_login_key=3Dm7WDZdTgVglYeON8BaRCy2bbtZ4PJPVrzTuO5kka=
Wu&utm_content=3Dchoice )
12 ( https://brilliant.org/practice/triangles-and-hexagons-2/?problem=3Dbas=
ic-2d-geometry-problem-163296&chapter=3Dintroduction-to-basic-2d-geometry&u=
tm_source=3Dbrilliant&utm_medium=3Demail&utm_campaign=3Dnls-ap1-q&utm_term=
=3Dgeo1-triandhex&auto_login_key=3Dm7WDZdTgVglYeON8BaRCy2bbtZ4PJPVrzTuO5kka=
Wu&utm_content=3Dchoice )
18 ( https://brilliant.org/practice/triangles-and-hexagons-2/?problem=3Dbas=
ic-2d-geometry-problem-163296&chapter=3Dintroduction-to-basic-2d-geometry&u=
tm_source=3Dbrilliant&utm_medium=3Demail&utm_campaign=3Dnls-ap1-q&utm_term=
=3Dgeo1-triandhex&auto_login_key=3Dm7WDZdTgVglYeON8BaRCy2bbtZ4PJPVrzTuO5kka=
Wu&utm_content=3Dchoice )

Where we end up:
( https://brilliant.org/practice/triangles-and-hexagons-2/?problem=3Dbasic-=
2d-geometry-problem-163296&chapter=3Dintroduction-to-basic-2d-geometry&utm_=
source=3Dbrilliant&utm_medium=3Demail&utm_campaign=3Dnls-ap1-q&utm_term=3Dg=
eo1-triandhex&auto_login_key=3Dm7WDZdTgVglYeON8BaRCy2bbtZ4PJPVrzTuO5kkaWu&u=
tm_content=3DpaneTextLink )
picture or diagram ( https://brilliant.org/practice/triangles-and-hexagons-=
2/?problem=3Dbasic-2d-geometry-problem-163296&chapter=3Dintroduction-to-bas=
ic-2d-geometry&utm_source=3Dbrilliant&utm_medium=3Demail&utm_campaign=3Dnls=
-ap1-q&utm_term=3Dgeo1-triandhex&auto_login_key=3Dm7WDZdTgVglYeON8BaRCy2bbt=
Z4PJPVrzTuO5kkaWu&utm_content=3DimageLink )

An equilateral triangle is placed in a regular hexagon so that its vertices=
 lie in the middle of the hexagon's sides.

Which is greater, the orange area or the blue area?

( https://brilliant.org/practice/triangles-and-hexagons-2/?problem=3Dbasic-=
2d-geometry-problem-163296&chapter=3Dintroduction-to-basic-2d-geometry&utm_=
source=3Dbrilliant&utm_medium=3Demail&utm_campaign=3Dnls-ap1-q&utm_term=3Dg=
eo1-triandhex&auto_login_key=3Dm7WDZdTgVglYeON8BaRCy2bbtZ4PJPVrzTuO5kkaWu&u=
tm_content=3DpaneTextLink )
* The orange area ( https://brilliant.org/practice/triangles-and-hexagons-2=
/?problem=3Dbasic-2d-geometry-problem-163296&chapter=3Dintroduction-to-basi=
c-2d-geometry&utm_source=3Dbrilliant&utm_medium=3Demail&utm_campaign=3Dnls-=
ap1-q&utm_term=3Dgeo1-triandhex&auto_login_key=3Dm7WDZdTgVglYeON8BaRCy2bbtZ=
4PJPVrzTuO5kkaWu&utm_content=3Dchoice )
* The blue area ( https://brilliant.org/practice/triangles-and-hexagons-2/?=
problem=3Dbasic-2d-geometry-problem-163296&chapter=3Dintroduction-to-basic-=
2d-geometry&utm_source=3Dbrilliant&utm_medium=3Demail&utm_campaign=3Dnls-ap=
1-q&utm_term=3Dgeo1-triandhex&auto_login_key=3Dm7WDZdTgVglYeON8BaRCy2bbtZ4P=
JPVrzTuO5kkaWu&utm_content=3Dchoice )
* They have the same area ( https://brilliant.org/practice/triangles-and-he=
xagons-2/?problem=3Dbasic-2d-geometry-problem-163296&chapter=3Dintroduction=
-to-basic-2d-geometry&utm_source=3Dbrilliant&utm_medium=3Demail&utm_campaig=
n=3Dnls-ap1-q&utm_term=3Dgeo1-triandhex&auto_login_key=3Dm7WDZdTgVglYeON8Ba=
RCy2bbtZ4PJPVrzTuO5kkaWu&utm_content=3Dchoice )

Start exploring ( https://brilliant.org/practice/triangles-and-hexagons-2/?=
problem=3Dbasic-2d-geometry-problem-163296&chapter=3Dintroduction-to-basic-=
2d-geometry&utm_source=3Dbrilliant&utm_medium=3Demail&utm_campaign=3Dnls-ap=
1-q&utm_term=3Dgeo1-triandhex&auto_login_key=3Dm7WDZdTgVglYeON8BaRCy2bbtZ4P=
JPVrzTuO5kkaWu&utm_content=3Dbutton )

Brilliant ( https://itunes.apple.com/us/app/apple-store/id913335252?pt=3D10=
5095803&ct=3Demail_footer&mt=3D8 )

Brilliant ( https://play.google.com/store/apps/details?id=3Dorg.brilliant.a=
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                .button-new td a.button-link:link,
                .button-new td a.button-link:visited,
                .button-new td a.button-link:hover,
                .button-new td a.button-link:active,
                .button-black td a.button-link:link,
                .button-black td a.button-link:visited,
                .button-black td a.button-link:hover,
                .button-black td a.button-link:active,
                .button-yellow td a.button-link:link,
                .button-yellow td a.button-link:visited,
                .button-yellow td a.button-link:hover,
                .button-yellow td a.button-link:active,
                .button-orange td a.button-link:link,
                .button-orange td a.button-link:visited,
                .button-orange td a.button-link:hover,
                .button-orange td a.button-link:active {
                    display: inline-block;
                    width: 100%;
                    border-style: solid;
                    color: #fff !important;
                    text-decoration: none;
                }
                .button td a.button-link:link,
                .button td a.button-link:visited,
                .button td a.button-link:hover,
                .button td a.button-link:active {
                    border-width: 12px 0;
                    border-color: #03a9f4;
                }
                .button-new td a.button-link:link,
                .button-new td a.button-link:visited,
                .button-new td a.button-link:hover,
                .button-new td a.button-link:active {
                    border-width: 14px 0;
                    border-color: #007aff;
                }
                .button-green td a.button-link:link,
                .button-green td a.button-link:visited,
                .button-green td a.button-link:hover,
                .button-green td a.button-link:active {
                    border-width: 12px 0;
                    border-color: #00b776;
                }
                .button-black td a.button-link:link,
                .button-black td a.button-link:visited,
                .button-black td a.button-link:hover,
                .button-black td a.button-link:active {
                    border-width: 12px 0;
                    border-color: #000;
                }
                .button-yellow td a.button-link:link,
                .button-yellow td a.button-link:visited,
                .button-yellow td a.button-link:hover,
                .button-yellow td a.button-link:active {
                    border-width: 14px 0;
                    border-color: #FFBA00;
                }
                .button-orange td a.button-link:link,
                .button-orange td a.button-link:visited,
                .button-orange td a.button-link:hover,
                .button-orange td a.button-link:active {
                    border-width: 11px 0;
                    border-color: #FA8A39;
                    font-size: 14px;
                }

        table.narrow-button-wrapper {
            width: 246px;
            min-width: 246px;
            margin: 0 auto;
            position: relative;
        }

        a.button-white:link,
        a.button-white:visited,
        a.button-white:hover,
        a.button-white:active {
            display: inline-block;
            padding: 12px 20px;
            border: 1px solid #000;
            font-weight: bold;
            font-size: 12px;
            line-height: 14px;
            color: #150F11 !important;
            text-transform: uppercase;
        }
=20=20=20=20=20=20=20=20
        a.button-black2:link,
        a.button-black2:visited,
        a.button-black2:hover,
        a.button-black2:active {
            display: inline-block;
            padding: 14px 60px;
            border: 0px solid #000;
            font-size: 15px;
            line-height: 20px;
            color: #FFFFFF !important;
            background-color: #000000;
            font-family: Soleil,Roboto,Helvetica,Arial,sans-serif;
            text-transform: uppercase;
        }

        /*-------------------- common --------------------*/

        table.table td {
            padding-top: 10px;
        }

        .center {
            text-align: center;
        }

        img.center {
            margin: 0 auto;
        }

        img.round {
            -webkit-border-radius: 50%;
               -moz-border-radius: 50%;
                    border-radius: 50%;
        }

        img.emoji {
            display: inline-block;
            margin: 0;
            vertical-align: middle;
            font-size: 1px;
            line-height: 1px;
        }

        .grey-logo td {
            padding: 30px 0 23px 0;
        }

        .black-logo {
            padding: 17px 0;
        }

        .preview-text {
            display: none;
            font-size: 1px;
            line-height: 1px;
            color: #f7f7f7;
        }

        .contains-long-links {
            word-break: break-all;
        }

        .p {
            margin-top: 13px;
            font-size: 14px;
            line-height: 21px;
            color: #777;
        }

        .p.note {
            font-size: 12px;
            line-height: 18px;
        }

        .checkmark {
            font-size: 24px;
            color: #00b776;
        }

        .outer {
            width: 448px;
            margin: 0 auto;
        }

        @media only screen and (max-width: 448px) {
            table[class=3D"body"] .outer {
                width: 100% !important;
            }
        }

        .inner {
            width: 306px;
            margin: 0 auto;
            position: relative;
        }

        @media only screen and (max-width: 320px) {
            table[class=3D"body"] .inner {
                width: 95% !important;
            }
        }


        /*-------------------- lists --------------------*/

        .list {
            width: 100%;
            min-width: 100%;
        }

            .list td {
                padding-top: 17px;
                padding-bottom: 2px;
                vertical-align: top;
            }

            .list td.bullet {
                width: 30px;
                text-align: center;
            }


        /*-------------------- header --------------------*/

        .header {
            padding-top: 13px;
            padding-bottom: 7px;
        }


        /*-------------------- content --------------------*/

        .content-wrapper {
            width: 448px;
            background: #fff;
        }

            .content {
                padding-top: 20px;
                padding-bottom: 28px;
                position: relative;
            }

        .problem-text {
            margin-top: 18px;
        }

            .problem-text .p {
                margin-top: 10px;
                font-size: 18px;
                line-height: 22px;
                color: #333;
            }
=20=20=20=20=20=20=20=20=20=20=20=20
        ul.choices {
            list-style: none;
            padding: 0;
            margin: 0;
        }
=20=20=20=20
            ul.choices li {
                list-style: none;
                padding: 0;
                margin: 0 0 12px 0;
            }
=20=20=20=20
                ul.choices a {
                    display: inline-block;
                    font-weight: bold;
                    font-size: 14px;
                    line-height: 21px;
                    background: #000;
                    -webkit-border-radius: 12px;
                       -moz-border-radius: 12px;
                            border-radius: 12px;
                }
=20=20=20=20
                ul.choices a:link,
                ul.choices a:visited,
                ul.choices a:hover,
                ul.choices a:active {
                    border-width: 7px 14px;
                    border-style: solid;
                    border-color: #000;
                    color: #fff !important;
                }

        ul.choices2 {
            list-style: none;
            padding: 0;
            margin: 0;
        }
=20=20=20=20
            ul.choices2 li {
                list-style: none;
                padding: 0;
                margin: 0 0 12px 0;
            }
=20=20=20=20
                ul.choices2 a {
                    display: inline-block;
                    font-weight: bold;
                    font-size: 14px;
                    line-height: 21px;
                    background: #FFF;
                    -webkit-border-radius: 12px;
                       -moz-border-radius: 12px;
                            border-radius: 12px;
                }
=20=20=20=20
                ul.choices2 a:link,
                ul.choices2 a:visited,
                ul.choices2 a:hover,
                ul.choices2 a:active {
                    border-width: 2px 2px;
                    border-style: solid;
                    border-color: #000;
                    padding-top: 7px;
                    padding-right: 14px;
                    padding-bottom: 7px;
                    padding-left: 14px;
                    color: #000 !important;
                }
        /*-------------------- separator --------------------*/

        table.separator,
        table.separator td {
            width: 100%;
            min-width: 100%;
        }

            .separator td {
                height: 1px;
                font-size: 1px;
                line-height: 1px;
                background: #bbb;
            }

        /*-------------------- small separator --------------------*/
=20=20=20=20
        table.small-separator,
        table.small-separator td {
            width: 130px;
            min-width: 130px;
        }
=20=20=20=20
            .small-separator td {
                height: 2px;
                font-size: 1px;
                line-height: 1px;
                background: #C4C4C4;
            }

        /*-------------------- choices --------------------*/

        .choices td {
            vertical-align: middle;
            padding-top: 9px;
            padding-bottom: 5px;
        }

        .choices td.radiobutton {
            width: 28px;
            padding-left: 12px;
            padding-right: 12px;
        }

            .choices td a:link,
            .choices td a:visited,
            .choices td a:hover,
            .choices td a:active {
                color: #333 !important;
            }


        /*-------------------- followers --------------------*/

        .follower {
            width: 100%;
            min-width: 100%;
        }

            .follower td {
                vertical-align: middle;
            }

            .follower td.avatar {
                width: 42px;
                padding-left: 4px;
                padding-right: 18px;
            }

        .follower-stats {
            width: 240px;
            min-width: 240px;
            margin: 0 auto;
        }

        @media only screen and (max-width: 240px) {
            table[class=3D"body"] .follower-stats {
                width: 100% !important;
                min-width: 0 !important;
            }
        }

            .follower-stats td {
                font-size: 13px;
                color: #777;
            }

            .follower-stats td.following,
            .follower-stats td.followers {
                width: 48%;
            }

            .follower-stats td.following {
                text-align: left;
            }

            .follower-stats td.followers {
                text-align: right;
            }

            .follower-stats td.spacer {
                width: 4%;
            }

                .follower-stats td strong {
                    color: #333;
                }


        /*-------------------- answer form --------------------*/

        .form-buttons {
            width: 100%;
            min-width: 100%;
        }

            .form-buttons td {
                font-size: 14px;
            }

            .form-buttons td.view-solutions,
            .form-buttons td.submit {
                width: 48%;
                padding-top: 14px;
            }

            .form-buttons td.spacer {
                width: 4%;
            }

                .answer .button {
                    border: 1px solid #777;
                }

                .answer .button,
                .answer .button td {
                    -webkit-border-radius: 5px;
                       -moz-border-radius: 5px;
                            border-radius: 5px;
                }

                    .answer .button td {
                        background: #f7f7f7;
                        color: #777;
                        text-align: left;
                    }

                        .answer .button td a.button-link:link,
                        .answer .button td a.button-link:visited,
                        .answer .button td a.button-link:hover,
                        .answer .button td a.button-link:active {
                            border-width: 11px 0;
                            border-color: #f7f7f7;
                            color: #777 !important;
                        }

                .view-solutions .button {
                    border: 1px solid #333;
                }

                    .view-solutions .button td {
                        background: #fff;
                        color: #333;
                    }

                        .view-solutions .button td a.button-link:link,
                        .view-solutions .button td a.button-link:visited,
                        .view-solutions .button td a.button-link:hover,
                        .view-solutions .button td a.button-link:active {
                            border-width: 11px 0;
                            border-color: #fff;
                            color: #333 !important;
                        }

                    .submit .button td {
                        border: 1px solid #03a9f4;
                    }

                        .submit .button td a.button-link:link,
                        .submit .button td a.button-link:visited,
                        .submit .button td a.button-link:hover,
                        .submit .button td a.button-link:active {
                            border-width: 11px 0;
                        }


        /*-------------------- set --------------------*/

        .set-header {
            margin-top: 7px;
        }

        .set-subheader {
            margin-top: 5px;
        }


        /*-------------------- mobile app badges --------------------*/

        .mobile-app-badges {
            width: 100%;
            min-width: 100%;
        }

            .mobile-app-badges td {
                padding-top: 28px;
                line-height: 10px;
            }
            .inner .mobile-app-badges td {
                padding-top: 8px;
            }

            .mobile-app-badges td.app-store,
            .mobile-app-badges td.google-play {
                width: 47%;
            }

            .mobile-app-badges td.app-store {
                text-align: right;
            }

            .mobile-app-badges td.google-play {
                text-align: left;
            }

            .mobile-app-badges td.spacer {
                width: 6%;
            }

        /*-------------------- footer --------------------*/

        .text-footer {
            color: #333;
        }

        .footer {
            padding-top: 14px;
            padding-bottom: 14px;
            font-size: 12px;
            line-height: 16px;
            color: #bbb;
            text-align: center;
        }

            .footer a:link,
            .footer a:visited,
            .footer a:hover,
            .footer a:active,
            a.footer-link:link,
            a.footer-link:visited,
            a.footer-link:hover,
            a.footer-link:active {
                color: #bbb !important;
            }

            .footer a,
            a.footer-link {
                text-decoration: underline;
            }
            .footer a:hover,
            a.footer-link:hover {
                text-decoration: none;
            }

        /*-------------------- potw difficulty buttons --------------------=
*/

        .potw-difficulty-table {
            width: 100%;
            margin-bottom: 10px;
        }
        .potw-difficulty-table td {
            width: 33.33%;
        }
        .potw-difficulty-option {
            display: block;
            width: 100%;
            padding: 4px 0;
            border: 1px solid #D4D4D4;
            text-align: center;
            color: #777777;
            font-size: 14px;
        }
        .potw-difficulty-option.active {
            background: #D8D8D8;
            color: #333;
        }

        /*-------------------- chapter list --------------------*/

        table.chapter {
            width: 306px;
            border-collapse: separate !important;
            box-shadow: 0 2px 4px #d2d8e0;
            border: 1px solid #DDD;
            -webkit-border-radius: 4px;
               -moz-border-radius: 4px;
                    border-radius: 4px;
        }

            table.chapter a {
                display: block;
            }

            td.chapter-image,
            td.chapter-text,
            td.chapter-progress {
                padding: 8px 0;
                vertical-align: middle;
            }

            td.chapter-image {
                width: 92px;
            }

                .chapter-image span,
                    .chapter-image img {
                        display: block;
                        width: 60px;
                        height: 60px;
                        -webkit-border-radius: 10px;
                           -moz-border-radius: 10px;
                                border-radius: 10px;
                    }

                .chapter-text h2 {
                    margin: 0 0 2px 0;
                    font-size: 16px;
                    font-weight: 700;
                    line-height: 1.3em;
                }

                    .chapter-text h2 a {
                        color: #333 !important;
                    }

                .chapter-text p {
                    margin: 0;
                    font-size: 13px;
                    line-height: 1.2em;
                }

                    .chapter-text p a {
                        color: #333 !important;
                    }

            td.chapter-progress {
                width: 67px;
            }

                .chapter-progress table,
                .chapter-progress table td {
                    width: 35px;
                    height: 35px;
                }

                    .chapter-progress table td {
                        background-color: #eee;
                        font-weight: bold;
                        font-size: 14px;
                        text-align: center;
                        vertical-align: middle;
                        -webkit-border-radius: 50%;
                           -moz-border-radius: 50%;
                                border-radius: 50%;
                    }
                    .chapter-progress.condensed table td {
                        font-size: 12px;
                    }

                        .chapter-progress table td a {
                            color: #0277bd !important;
                        }

        /*-------------------- quiz gallery --------------------*/

        table.quiz-gallery {
            width: 306px;
            border-collapse: separate !important;
            margin: 0 auto;
            position: relative;
        }

            table.quiz-gallery a {
                display: block;
            }

            td.quiz-gallery-column {
                width: 126px;
                padding-left: 8px;
                padding-right: 8px;
            }

            td.quiz-gallery-column,
            td.quiz-gutter {
                border-bottom: 1px solid #fff;
            }

            td.quiz-gutter {
                width: 18px;
            }

            td.quiz-card {
                padding-top: 16px;
                padding-bottom: 16px;
                box-shadow: 0 2px 4px #d2d8e0;
                border: 1px solid #DDD;
                -webkit-border-radius: 4px;
                   -moz-border-radius: 4px;
                        border-radius: 4px;
            }

                table.quiz-image {
                    margin: 0 auto;
                    position: relative;
                }

                table.quiz-image,
                table.quiz-image td {
                    width: 100px;
                    height: 100px;
                }
                .quiz-card.intro table.quiz-image,
                .quiz-card.intro table.quiz-image td {
                    width: 126px;
                    height: 126px;
                }

                    table.quiz-image td {
                        vertical-align: middle;
                    }

                    table.quiz-image img {
                        display: block;
                        max-width: 100px;
                        max-height: 100px;
                    }
                    .quiz-card.intro table.quiz-image img {
                        max-width: 126px;
                        max-height: 126px;
                    }

                table.quiz-title {
                    width: 126px;
                }

                table.quiz-title,
                table.quiz-title td {
                    height: 65px;
                }
                .quiz-card.intro table.quiz-title,
                .quiz-card.intro table.quiz-title td {
                    height: 39px;
                }

                    .quiz-title td {
                        vertical-align: middle;
                    }

                    .quiz-title h2 {
                        line-height: 19px;
                        word-wrap: break-word;
                        word-break: break-word;
                    }

                        .quiz-title h2 a {
                            color: #333 !important;
                        }

                table.quiz-progress {
                    width: 126px;
                }

                table.quiz-progress,
                td.quiz-progress-content {
                    height: 41px;
                    vertical-align: bottom;
                }

                    table.quiz-progress img {
                        display: block;
                    }

                    table.quiz-items {
                        width: 126px;
                    }

                    table.quiz-items,
                    table.quiz-items td,
                    table.quiz-items td a {
                        height: 8px;
                    }

                        table.quiz-items td {
                            width: 126px;
                            background: #e8e8e8;
                            border-right: 1px solid #fbfbfb;
                            font-size: 1px;
                            line-height: 1px;
                        }
                        table.quiz-items td.completed {
                            background: #ffde5c;
                        }

                    table.quiz-number {
                        width: 126px;
                    }

                        .quiz-number td {
                            padding-top: 8px;
                            font-size: 13px;
                            color: #777;
                            text-align: center;
                        }

                            .quiz-number td a {
                                color: #333 !important;
                            }

        /*-------------------- chapter map --------------------*/

        table.chapter.completed {
            position: relative;
            margin: 0 auto;
            box-shadow: none;
            border-width: 2px;
        }

        table.chapter-quizzes-connector {
            position: relative;
            width: 306px;
            margin: 0 auto;
        }

            table.chapter-quizzes-connector,
            table.chapter-quizzes-connector td {
                height: 18px;
            }

            .chapter-quizzes-connector td {
                width: 153px;
            }

            .chapter-quizzes-connector .left {
                border-right: 2px solid #f0f0f0;
            }

        table.completed-quizzes {
            margin: 0 auto;
            border: 2px solid #f0f0f0;
            position: relative;
        }

        td.completed-quizzes-content {
            padding-bottom: 18px;
        }

            table.completed-quizzes table.quiz-gallery {
                width: 264px;
            }

            .completed-quizzes td.quiz-gallery-column {
                width: 84px;
                padding-top: 8px;
                padding-bottom: 8px;
            }
            .completed-quizzes td.quiz-gallery-column.empty {
                width: 100px;
                padding: 0;
            }

                .completed-quizzes table.quiz-image,
                .completed-quizzes table.quiz-image td {
                    width: 50px;
                    height: 50px;
                }

                    .completed-quizzes table.quiz-image img {
                        display: block;
                        max-width: 50px;
                        max-height: 50px;
                    }

                .completed-quizzes table.quiz-title,
                .completed-quizzes table.quiz-progress {
                    width: 84px;
                }

                    .completed-quizzes .quiz-title h2 {
                        font-size: 12px;
                        line-height: 15px;
                    }

                .completed-quizzes table.quiz-progress,
                .completed-quizzes td.quiz-progress-content {
                    height: 17px;
                }

            table.completed-quiz-connector {
                border-bottom: 2px solid #f0f0f0;
            }

                table.completed-quiz-connector,
                table.completed-quiz-connector td {
                    width: 18px;
                    height: 75px;
                }
                .empty table.completed-quiz-connector,
                .empty table.completed-quiz-connector td {
                    width: 102px;
                }

        /*-------------------- daily problems --------------------*/

        .daily-problems-header .col-right {
            text-align: right;
            font-size: 17px;
        }

        .daily-problems-header td.spacer {
            width: 20px;
        }

        .daily-problems-header .date {
            font-size: 13px;
            color: #919191;
        }

            .daily-problems-header .inner td {
                padding: 20px 0;
                vertical-align: middle;
            }

        .daily-problem-content,
        .more-problems {
            border-top: 1px solid #F0F0F0;
        }

            .daily-problem-content .track-name {
                margin: 0;
                font-weight: 500;
                font-size: 13px;
                text-transform: uppercase;
                color: #899098;
            }

            .daily-problem-content .problem-title {
                margin: 15px 0 0 0;
                font-weight: bold;
                font-size: 20px;
                color: #1F1F1F !important;
            }

            .daily-problem-content .preview {
                padding-bottom: 10px;
            }

            .daily-problem-content .problem-text .p {
                font-size: 15px;
                line-height: 26px;
            }

=20=20=20=20=20=20=20=20=20=20=20=20
             .daily-problem-content .problem-title {
                font-size: 28px;
                line-height: 34px;
            }
            .daily-problem-content .problem-text .p {
                font-size: 20px;
                line-height: 28px;
            }

            .daily-problem-content .problem-text .image-caption {
                display: inline-block;
                text-align: left;
            }

=20=20=20=20=20=20=20=20=20=20=20=20

            .daily-problem-content .more {
                font-weight: bold;
                color: #0C6AC7;
            }

            .daily-problem-content table.button {
                -webkit-border-radius: 3px;
                -moz-border-radius: 3px;
                -ms-border-radius: 3px;
                border-radius: 3px;
            }

                .daily-problem-content table.button td {
                    background: #007AFF;
                }

                    .daily-problem-content table.button td a.button-link:li=
nk,
                    .daily-problem-content table.button td a.button-link:vi=
sited,
                    .daily-problem-content table.button td a.button-link:ho=
ver,
                    .daily-problem-content table.button td a.button-link:ac=
tive {
                        border-width: 14px 0;
                        border-color: #007AFF;
                    }

        a.snooze-reminders:link,
        a.snooze-reminders:visited,
        a.snooze-reminders:hover,
        a.snooze-reminders:active {
            color: #0C6AC7 !important;
        }

        .top-daily-problem-content h2,
        .top-daily-problem-content h3,
        .more-problems h2 {
            margin-top: 10px;
            font-weight: bold;
            color: #0C6AC7;
        }

        .top-daily-problem-content h2 {
            font-size: 17px;
        }

        .top-daily-problem-content h3 {
            font-size: 15px;
        }

        .top-daily-problem-content .problem-text .p {
            font-size: 18px;
        }

        .more-problems h2 {
            margin-bottom: 8px;
            font-size: 16px;
        }

        .top-daily-problem-content .track-name {
            margin-top: 12px;
        }

        .top-daily-problem-content .preview {
            margin-top: 0;
        }

        table.problem-card {
            margin-bottom: 10px;
            border-collapse: separate !important;
            border: 1px solid #BBB;
            -webkit-border-radius: 10px;
            -moz-border-radius: 10px;
            -ms-border-radius: 10px;
            border-radius: 10px;
            -webkit-box-shadow: 0 1px 4px #BBB;
            -moz-box-shadow: 0 1px 4px #BBB;
            -ms-box-shadow: 0 1px 4px #BBB;
            box-shadow: 0 1px 4px #BBB;
        }

            .problem-card td {
                vertical-align: middle;
            }

            .problem-card td.spacer {
                width: 24px;
            }

            .problem-card td.track {
                padding: 10px 0 6px 0;
                font-weight: 500;
                font-size: 11px;
                letter-spacing: 0.1em;
                text-transform: uppercase;
            }

                .problem-card td.track,
                .problem-card td.track a:link,
                .problem-card td.track a:visited,
                .problem-card td.track a:hover,
                .problem-card td.track a:active {
                    color: #1F1F1F !important;
                }

            .problem-card td.title {
                width: 176px;
                font-weight: bold;
                font-size: 22px;
                line-height: 27px;
                color: #333;
            }

                .problem-card td.title,
                .problem-card td.title a:link,
                .problem-card td.title a:visited,
                .problem-card td.title a:hover,
                .problem-card td.title a:active {
                    color: #333 !important;
                }

            .problem-card td.img {
                width: 80px;
                text-align: right;
            }

                .problem-card td.img table {
                    margin-left: 16px;
                    overflow: hidden;
                    -webkit-border-radius: 8px;
                    -moz-border-radius: 8px;
                    -ms-border-radius: 8px;
                    border-radius: 8px;
                }


                .problem-card td.img table,
                .problem-card td.img table td {
                    width: 64px;
                }

            .problem-card td.text {
                padding: 12px 0 8px 0;
                border-bottom: 1px solid #ddd;
                font-size: 13px;
                line-height: 21px;
                color: #1F1F1F;
            }

                .problem-card td.text,
                .problem-card td.text a:link,
                .problem-card td.text a:visited,
                .problem-card td.text a:hover,
                .problem-card td.text a:active {
                    color: #1F1F1F !important;
                }

            .problem-card td.popularity {
                font-weight: 500;
                font-size: 12px;
                color: #6D7E8E;
            }

                .problem-card td.popularity,
                .problem-card td.popularity a:link,
                .problem-card td.popularity a:visited,
                .problem-card td.popularity a:hover,
                .problem-card td.popularity a:active {
                    color: #6D7E8E !important;
                }

            .problem-card td.action {
                padding: 12px 0;
            }

                .problem-card td.action .button {
                    border: 1px solid #005FFA;
                    -webkit-box-shadow: none;
                    -moz-box-shadow: none;
                    -ms-box-shadow: none;
                    box-shadow: none;
                }

                .problem-card td.action .button,
                .problem-card td.action .button td {
                    -webkit-border-radius: 4px;
                    -moz-border-radius: 4px;
                    -ms-border-radius: 4px;
                    border-radius: 4px;
                }

                    .problem-card td.action .button td {
                        padding: 0 5px;
                        background: #fff;
                        font-weight: bold;
                        font-size: 13px;
                        color: #005FFA;
                        white-space: nowrap;
                    }

                        .problem-card td.action .button td a.button-link:li=
nk,
                        .problem-card td.action .button td a.button-link:vi=
sited,
                        .problem-card td.action .button td a.button-link:ho=
ver,
                        .problem-card td.action .button td a.button-link:ac=
tive {
                            border-width: 4px 0;
                            border-color: #fff;
                            color: #005FFA !important;
                        }

            .set-reminders table.button {
                -webkit-border-radius: 3px;
                -moz-border-radius: 3px;
                -ms-border-radius: 3px;
                border-radius: 3px;
            }

                .set-reminders table.button td {
                    background: #005FFA;
                    font-size: 13px;
                }

                    .set-reminders table.button td a.button-link:link,
                    .set-reminders table.button td a.button-link:visited,
                    .set-reminders table.button td a.button-link:hover,
                    .set-reminders table.button td a.button-link:active {
                        border-color: #005FFA;
                    }

                .set-reminders table.button img {
                    vertical-align: -2px;
                }

        /*-------------------- gifting emails --------------------*/

        .gifting-header {
            background: #1f1f1f;
        }
=20=20=20=20=20=20=20=20
        .gifting-header.blue-bg {
            background: #3A7CC0;
        }

            .gifting-header td {
                vertical-align: middle;
            }
            .gifting-header td.gifting-header-text {
                width: 55.35%;
            }
            .gifting-header td.gifting-header-image {
                width: 44.65%;
                text-align: right;
                vertical-align: bottom;
            }

                .gifting-header-text table {
                    width: 100%;
                }

                    .gifting-header-text table td {
                        height: auto;
                        padding: 16px 0 16px 22px;
                        font-weight: bold;
                        font-size: 23px;
                        line-height: 27px;
                        word-wrap: break-word;
                        word-break: break-word;
                        color: #fff;
                    }

                        .gifting-header-text a:link,
                        .gifting-header-text a:visited,
                        .gifting-header-text a:hover,
                        .gifting-header-text a:active {
                            color: #fff !important;
                        }

                    .gifting-header-image a,
                    .gifting-header-image img {
                        display: block;
                        font-size: 1px;
                        line-height: 1px;
                    }

                    .gifting-header-image img {
                        max-width: 100%;
                        width: 100%;
                    }

        /*-------------------- NUX emails --------------------*/

        .nux-intro-blurb .content {
            font-size: 17px;
            line-height: 29px;
        }

        .nux-problem-content .track-name {
            font-size: 12px;
        }

        .nux-problem-content .problem-title {
            font-size: 18px;
        }

        .nux-problem-content .button td {
            font-size: 17px;
        }

        .suggested-chapter {
            padding: 30px 0;
            border-top: 1px solid #F0F0F0;
        }

            .suggested-chapter h3 {
                width: 342px;
                margin: 0 auto 28px auto;
                font-size: 16px;
                font-weight: bold;
                text-align: left;
            }

        table.chapter-card {
            width: 342px;
            overflow: hidden;
            border-radius: 8px;
            box-shadow: 0 4px 4px rgba(0, 0, 0, 0.25);
        }

            td.chapter-card-text {
                width: 208px;
                padding: 24px 0 23px 30px;
            }

                .chapter-card-text h4 {
                    padding-bottom: 9px;
                    margin-bottom: 8px;
                    border-bottom: 1px solid #aaa;
                    font-weight: bold;
                    font-size: 24px;
                    line-height: 30px;
                }

                    .chapter-card-text h4 a {
                        color: #fff !important;
                    }

                .chapter-card-text table {
                    width: 100%;
                }

                    .chapter-card-text table td {
                        padding: 2px 0;
                        font-size: 12px;
                        line-height: 15px;
                    }
                    .chapter-card-text table td.left {
                        width: 63px;
                        padding-left: 4px;
                    }

                        .chapter-card-text table td a {
                            color: #fff !important;
                        }


            td.chapter-card-image {
                width: 85px;
                padding: 24px 0 0 20px;
                vertical-align: top;
            }

                .chapter-card-image table,
                .chapter-card-image table td {
                    width: 64px;
                }

                .chapter-card-image table {
=20=20=20=20=20=20=20=20=20=20=20=20=20=20=20=20=20=20=20=20
                    background: #ccc;
                    background: url('https://static.brilliant.org/static/sy=
nc/email-images/nux/chapter-image-bg.png') repeat;
                    background: rgba(255, 255, 255, 0.13);
                    border-radius: 8px;
                    overflow: hidden;
                }

                    .chapter-card-image table td {
                        padding: 17px 0;
                        vertical-align: middle;
                    }

                        .chapter-card-image table table,
                        .chapter-card-image table table td {
                            width: 52px;
                        }

                        .chapter-card-image table table {
                            border-radius: 50%;
                            overflow: hidden;
                        }

                            .chapter-card-image table table td {
                                padding: 6px 0;
                            }

                .chapter-card-image img {
                    border-radius: 50%;
                    overflow: hidden;
                }

        /*-------------------- 7 Day Challenge --------------------*/

        .seven-day-challenge .daily-problems-header td.spacer {
            width: 10px;
        }

        .seven-day-challenge .daily-problems-header .col-right {
            padding: 16px 0;
        }

        .seven-day-challenge .daily-problems-header .col-right h1 {
            font-weight: bold;
            font-size: 16px;
            line-height: 28px;
        }

        .seven-day-challenge .daily-problems-header .date {
            font-size: 12px;
            line-height: 16px;
            color: #919191;
        }

        /*-------------------- 7 Day Challenge endstate -------------------=
-*/

        .seven-day-challenge-endstate {
            line-height: 21px;
        }

        .seven-day-challenge-endstate h1 {
            font-weight: bold;
            font-size: 24px;
            line-height: 28px;
            text-align: center;
        }

            .seven-day-challenge-endstate h1 .emoji {
                vertical-align: -1px;
            }

            .seven-day-challenge-endstate p {
                margin: 4px 0;
            }

        .seven-day-challenge-header {
            background: #d2e9f8 url('https://static.brilliant.org/static/sy=
nc/email-images/nux/7-day-challenge-header-bg.png') center top repeat-x;
        }

            .seven-day-challenge-header .inner td {
                padding: 14px 0;
                font-size: 17px;
                line-height: 28px;
            }

                .seven-day-challenge-header h1 {
                    margin-top: 12px;
                    font-weight: bold;
                    font-size: 24px;
                    line-height: 28px;
                }

    </style>
</head>





<body style=3D"width: 100% !important; height: 100% !important; min-width: =
100%; line-height: 100% !important; -webkit-text-size-adjust: 100%; -ms-tex=
t-size-adjust: 100%; background-color: #f7f7f7; font-family: &#39;Helvetica=
&#39;, &#39;Arial&#39;, sans-serif; font-weight: normal; font-size: 15px; c=
olor: #333; margin: 0; padding: 0;" bgcolor=3D"#f7f7f7"><table style=3D"bac=
kground-color: #f7f7f7; width: 100% !important; height: 100% !important; mi=
n-width: 100%; line-height: 100% !important; -webkit-text-size-adjust: 100%=
; -ms-text-size-adjust: 100%; border-collapse: collapse !important; max-wid=
th: 100%; mso-table-lspace: 0pt; mso-table-rspace: 0pt; border-spacing: 0; =
vertical-align: top; text-align: left; font-family: &#39;Helvetica&#39;, &#=
39;Arial&#39;, sans-serif; font-weight: normal; font-size: 15px; color: #33=
3; margin: 0; padding: 0;" class=3D"body" bgcolor=3D"#f7f7f7"><tbody><tr st=
yle=3D"vertical-align: top; text-align: left; margin: 0; padding: 0;" align=
=3D"left"><td align=3D"center" valign=3D"top" class=3D"center" style=3D"bor=
der-collapse: collapse !important; vertical-align: top; text-align: center;=
 font-family: &#39;Helvetica&#39;, &#39;Arial&#39;, sans-serif; font-weight=
: normal; font-size: 15px; line-height: 18px; color: #333; margin: 0; paddi=
ng: 0;"><center style=3D"width: 100%; min-width: 0 !important;">
    <div class=3D"preview-text center" style=3D"font-family: &#39;Helvetica=
&#39;, &#39;Arial&#39;, sans-serif; font-weight: normal; font-size: 1px; li=
ne-height: 1px; color: #f7f7f7; text-align: center; display: none; margin: =
0; padding: 0;" align=3D"center">More often than not, the art of solving co=
mplex geometry problems comes down to triangles. How do you split up figure=
s into triangles, and how does that help you solve the problem?</div>

=20=20=20=20
    <table class=3D"outer" style=3D"border-collapse: collapse !important; m=
ax-width: 100%; mso-table-lspace: 0pt; mso-table-rspace: 0pt; border-spacin=
g: 0; vertical-align: top; text-align: left; width: 448px; margin: 0 auto; =
padding: 0;"><tbody><tr style=3D"vertical-align: top; text-align: left; mar=
gin: 0; padding: 0;" align=3D"left"><td align=3D"center" class=3D"black-log=
o content-wrapper center" style=3D"border-collapse: collapse !important; ve=
rtical-align: top; text-align: center; font-family: &#39;Helvetica&#39;, &#=
39;Arial&#39;, sans-serif; font-weight: normal; font-size: 15px; line-heigh=
t: 18px; color: #333; width: 448px; background-color: #fff; margin: 0; padd=
ing: 17px 0;" bgcolor=3D"#fff" valign=3D"top"><center style=3D"width: 100%;=
 min-width: 0 !important;">
        <a href=3D"https://t.brilliant.org/e/c/eyJlbWFpbF9pZCI6IlJQNG9BUUFC=
Y0tQWF93d2dSR2R3SkZzREhBUk4iLCJocmVmIjoiaHR0cHM6Ly9icmlsbGlhbnQub3JnL3ByYWN=
0aWNlL3RyaWFuZ2xlcy1hbmQtaGV4YWdvbnMtMi8_cHJvYmxlbT1iYXNpYy0yZC1nZW9tZXRyeS=
1wcm9ibGVtLTE2MzI5Nlx1MDAyNmNoYXB0ZXI9aW50cm9kdWN0aW9uLXRvLWJhc2ljLTJkLWdlb=
21ldHJ5XHUwMDI2dXRtX3NvdXJjZT1icmlsbGlhbnRcdTAwMjZ1dG1fbWVkaXVtPWVtYWlsXHUw=
MDI2dXRtX2NhbXBhaWduPW5scy1hcDEtcVx1MDAyNnV0bV90ZXJtPWdlbzEtdHJpYW5kaGV4XHU=
wMDI2YXV0b19sb2dpbl9rZXk9bTdXRFpkVGdWZ2xZZU9OOEJhUkN5MmJidFo0UEpQVnJ6VHVPNW=
trYVd1XHUwMDI2dXRtX2NvbnRlbnQ9YnJpbGxpYW50bG9nbyIsImxpbmtfaWQiOjE5Mzk0Mjc4N=
CwicG9zaXRpb24iOjB9/7fe155d5bfada6dd4bc576090fc5d26dfe5147312c128c2700b14ce=
79b20e3db" style=3D"color: #03a9f4 !important; text-decoration: none;">
            <img class=3D"center" src=3D"https://static.brilliant.org/stati=
c/sync/email-images/logos/large-black-logo-x3.png" width=3D"162" height=3D"=
37" border=3D"0" title=3D"Brilliant" alt=3D"Brilliant" style=3D"max-width: =
100%; height: auto; line-height: 100%; outline: none; text-decoration: none=
; -ms-interpolation-mode: bicubic; text-align: center; margin: 0 auto; bord=
er: 0 none;"/>
        </a>
    </center></td></tr></tbody></table>
=20=20=20=20

=20=20=20=20
    <table class=3D"outer" style=3D"border-collapse: collapse !important; m=
ax-width: 100%; mso-table-lspace: 0pt; mso-table-rspace: 0pt; border-spacin=
g: 0; vertical-align: top; text-align: left; width: 448px; margin: 0 auto; =
padding: 0;"><tbody><tr style=3D"vertical-align: top; text-align: left; mar=
gin: 0; padding: 0;" align=3D"left"><td align=3D"center" class=3D"content-w=
rapper center" style=3D"border-collapse: collapse !important; vertical-alig=
n: top; text-align: center; font-family: &#39;Helvetica&#39;, &#39;Arial&#3=
9;, sans-serif; font-weight: normal; font-size: 15px; line-height: 18px; co=
lor: #333; width: 448px; background-color: #fff; margin: 0; padding: 0;" bg=
color=3D"#fff" valign=3D"top"><center style=3D"width: 100%; min-width: 0 !i=
mportant;">
        <a href=3D"https://t.brilliant.org/e/c/eyJlbWFpbF9pZCI6IlJQNG9BUUFC=
Y0tQWF93d2dSR2R3SkZzREhBUk4iLCJocmVmIjoiaHR0cHM6Ly9icmlsbGlhbnQub3JnL3ByYWN=
0aWNlL3RyaWFuZ2xlcy1hbmQtaGV4YWdvbnMtMi8_cHJvYmxlbT1iYXNpYy0yZC1nZW9tZXRyeS=
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21ldHJ5XHUwMDI2dXRtX3NvdXJjZT1icmlsbGlhbnRcdTAwMjZ1dG1fbWVkaXVtPWVtYWlsXHUw=
MDI2dXRtX2NhbXBhaWduPW5scy1hcDEtcVx1MDAyNnV0bV90ZXJtPWdlbzEtdHJpYW5kaGV4XHU=
wMDI2YXV0b19sb2dpbl9rZXk9bTdXRFpkVGdWZ2xZZU9OOEJhUkN5MmJidFo0UEpQVnJ6VHVPNW=
trYVd1XHUwMDI2dXRtX2NvbnRlbnQ9aGVhZGVySW1hZ2UiLCJsaW5rX2lkIjoxOTM5NDI3ODUsI=
nBvc2l0aW9uIjoxfQ/3beee395ac81b2c172b427d54442ea5f8d836e5ac11008de73d8626f1=
e129733" style=3D"color: #03a9f4 !important; text-decoration: none;">
            <img src=3D"https://static.brilliant.org/static/sync/email-imag=
es/quiz_emails/geo1/trihex_blueorange.png" class=3D"center" width=3D"448" b=
order=3D"0" alt=3D"" style=3D"max-width: 100%; height: auto; line-height: 1=
00%; outline: none; text-decoration: none; -ms-interpolation-mode: bicubic;=
 text-align: center; margin: 0 auto; border: 0 none;"/>
        </a>
    </center></td></tr></tbody></table>
=20=20=20=20

=20=20=20=20
    <table class=3D"outer" style=3D"border-collapse: collapse !important; m=
ax-width: 100%; mso-table-lspace: 0pt; mso-table-rspace: 0pt; border-spacin=
g: 0; vertical-align: top; text-align: left; width: 448px; margin: 0 auto; =
padding: 0;"><tbody><tr style=3D"vertical-align: top; text-align: left; mar=
gin: 0; padding: 0;" align=3D"left"><td align=3D"center" class=3D"content-w=
rapper center problem-content daily-problem-content nux-problem-content" st=
yle=3D"border-collapse: collapse !important; vertical-align: top; text-alig=
n: center; font-family: &#39;Helvetica&#39;, &#39;Arial&#39;, sans-serif; f=
ont-weight: normal; font-size: 15px; line-height: 18px; color: #333; width:=
 448px; background-color: #fff; border-top-width: 1px; border-top-color: #F=
0F0F0; border-top-style: solid; margin: 0; padding: 0;" bgcolor=3D"#fff" va=
lign=3D"top"><center style=3D"width: 100%; min-width: 0 !important;">
    <table class=3D"inner" style=3D"border-collapse: collapse !important; m=
ax-width: 100%; mso-table-lspace: 0pt; mso-table-rspace: 0pt; border-spacin=
g: 0; vertical-align: top; text-align: left; width: 306px; position: relati=
ve; margin: 0 auto; padding: 0;"><tbody><tr style=3D"vertical-align: top; t=
ext-align: left; margin: 0; padding: 0;" align=3D"left"><td class=3D"conten=
t" style=3D"border-collapse: collapse !important; vertical-align: top; text=
-align: left; font-family: &#39;Helvetica&#39;, &#39;Arial&#39;, sans-serif=
; font-weight: normal; font-size: 15px; line-height: 18px; color: #333; pos=
ition: relative; margin: 0; padding: 20px 0 28px;" align=3D"left" valign=3D=
"top">

    <h1 style=3D"font-family: &#39;Helvetica&#39;, &#39;Arial&#39;, sans-se=
rif; font-weight: normal; font-size: 18px; line-height: 22px; color: #333 !=
important; margin: 0; padding: 0;"><b></b></h1>


<a href=3D"https://t.brilliant.org/e/c/eyJlbWFpbF9pZCI6IlJQNG9BUUFCY0tQWF93=
d2dSR2R3SkZzREhBUk4iLCJocmVmIjoiaHR0cHM6Ly9icmlsbGlhbnQub3JnL3ByYWN0aWNlL3R=
yaWFuZ2xlcy1hbmQtaGV4YWdvbnMtMi8_cHJvYmxlbT1iYXNpYy0yZC1nZW9tZXRyeS1wcm9ibG=
VtLTE2MzI5Nlx1MDAyNmNoYXB0ZXI9aW50cm9kdWN0aW9uLXRvLWJhc2ljLTJkLWdlb21ldHJ5X=
HUwMDI2dXRtX3NvdXJjZT1icmlsbGlhbnRcdTAwMjZ1dG1fbWVkaXVtPWVtYWlsXHUwMDI2dXRt=
X2NhbXBhaWduPW5scy1hcDEtcVx1MDAyNnV0bV90ZXJtPWdlbzEtdHJpYW5kaGV4XHUwMDI2YXV=
0b19sb2dpbl9rZXk9bTdXRFpkVGdWZ2xZZU9OOEJhUkN5MmJidFo0UEpQVnJ6VHVPNWtrYVd1XH=
UwMDI2dXRtX2NvbnRlbnQ9cGFuZVRleHRMaW5rIiwibGlua19pZCI6MTkzOTQyODg3LCJwb3Npd=
GlvbiI6Mn0/2e3866cee60ba5f29b33272fd62af18bc63ef9594198d02acf497b4ac3b5143a=
" style=3D"color: #03a9f4 !important; text-decoration: none;"><div class=3D=
"problem-text" style=3D"font-family: &#39;Helvetica&#39;, &#39;Arial&#39;, =
sans-serif; font-weight: normal; font-size: 15px; line-height: 18px; color:=
 #333; margin: 18px 0 0; padding: 0;"><div class=3D"p" style=3D"font-family=
: &#39;Helvetica&#39;, &#39;Arial&#39;, sans-serif; font-weight: normal; fo=
nt-size: 20px; line-height: 28px; color: #333; margin: 10px 0 0; padding: 0=
;">
Take a look at this regular hexagon, and try to see if there=E2=80=99s any =
relation to the blue and orange areas.<br style=3D"font-family: &#39;Helvet=
ica&#39;, &#39;Arial&#39;, sans-serif; font-weight: normal; font-size: 15px=
; line-height: 18px; color: #333;"/><br style=3D"font-family: &#39;Helvetic=
a&#39;, &#39;Arial&#39;, sans-serif; font-weight: normal; font-size: 15px; =
line-height: 18px; color: #333;"/>
</div></div></a>

<center style=3D"width: 100%; min-width: 0 !important;"><a href=3D"https://=
t.brilliant.org/e/c/eyJlbWFpbF9pZCI6IlJQNG9BUUFCY0tQWF93d2dSR2R3SkZzREhBUk4=
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b5d1f12edecc910ba42fa7371d0bf0cd2fc978164d8bb8c8b" style=3D"color: #03a9f4 =
!important; text-decoration: none;"><img width=3D"250" class=3D"center" src=
=3D"https://static.brilliant.org/static/sync/email-images/quiz_emails/geo1/=
hex1.png" alt=3D"picture or diagram" title=3D"picture or diagram" style=3D"=
max-width: 100%; height: auto; line-height: 100%; outline: none; text-decor=
ation: none; -ms-interpolation-mode: bicubic; text-align: center; margin: 0=
 auto; border: 0 none;"/></a></center>

<br style=3D"font-family: &#39;Helvetica&#39;, &#39;Arial&#39;, sans-serif;=
 font-weight: normal; font-size: 15px; line-height: 18px; color: #333;"/>
<a href=3D"https://t.brilliant.org/e/c/eyJlbWFpbF9pZCI6IlJQNG9BUUFCY0tQWF93=
d2dSR2R3SkZzREhBUk4iLCJocmVmIjoiaHR0cHM6Ly9icmlsbGlhbnQub3JnL3ByYWN0aWNlL3R=
yaWFuZ2xlcy1hbmQtaGV4YWdvbnMtMi8_cHJvYmxlbT1iYXNpYy0yZC1nZW9tZXRyeS1wcm9ibG=
VtLTE2MzI5Nlx1MDAyNmNoYXB0ZXI9aW50cm9kdWN0aW9uLXRvLWJhc2ljLTJkLWdlb21ldHJ5X=
HUwMDI2dXRtX3NvdXJjZT1icmlsbGlhbnRcdTAwMjZ1dG1fbWVkaXVtPWVtYWlsXHUwMDI2dXRt=
X2NhbXBhaWduPW5scy1hcDEtcVx1MDAyNnV0bV90ZXJtPWdlbzEtdHJpYW5kaGV4XHUwMDI2YXV=
0b19sb2dpbl9rZXk9bTdXRFpkVGdWZ2xZZU9OOEJhUkN5MmJidFo0UEpQVnJ6VHVPNWtrYVd1XH=
UwMDI2dXRtX2NvbnRlbnQ9cGFuZVRleHRMaW5rIiwibGlua19pZCI6MTkzOTQyODg3LCJwb3Npd=
GlvbiI6NH0/1f517131228d6d32a024695e07e7c99e7d0f98fd5980a574aeaaef30bd9cafda=
" style=3D"color: #03a9f4 !important; text-decoration: none;"><div class=3D=
"problem-text" style=3D"font-family: &#39;Helvetica&#39;, &#39;Arial&#39;, =
sans-serif; font-weight: normal; font-size: 15px; line-height: 18px; color:=
 #333; margin: 18px 0 0; padding: 0;"><div class=3D"p" style=3D"font-family=
: &#39;Helvetica&#39;, &#39;Arial&#39;, sans-serif; font-weight: normal; fo=
nt-size: 20px; line-height: 28px; color: #333; margin: 10px 0 0; padding: 0=
;">
More often than not, the art of solving complex geometry problems comes dow=
n to triangles. How do you split up figures into triangles, and how does th=
at help you solve the problem?
</div></div></a>
<br style=3D"font-family: &#39;Helvetica&#39;, &#39;Arial&#39;, sans-serif;=
 font-weight: normal; font-size: 15px; line-height: 18px; color: #333;"/>
<center style=3D"width: 100%; min-width: 0 !important;"><a href=3D"https://=
t.brilliant.org/e/c/eyJlbWFpbF9pZCI6IlJQNG9BUUFCY0tQWF93d2dSR2R3SkZzREhBUk4=
iLCJocmVmIjoiaHR0cHM6Ly9icmlsbGlhbnQub3JnL3ByYWN0aWNlL3RyaWFuZ2xlcy1hbmQtaG=
V4YWdvbnMtMi8_cHJvYmxlbT1iYXNpYy0yZC1nZW9tZXRyeS1wcm9ibGVtLTE2MzI5Nlx1MDAyN=
mNoYXB0ZXI9aW50cm9kdWN0aW9uLXRvLWJhc2ljLTJkLWdlb21ldHJ5XHUwMDI2dXRtX3NvdXJj=
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hcDEtcVx1MDAyNnV0bV90ZXJtPWdlbzEtdHJpYW5kaGV4XHUwMDI2YXV0b19sb2dpbl9rZXk9bT=
dXRFpkVGdWZ2xZZU9OOEJhUkN5MmJidFo0UEpQVnJ6VHVPNWtrYVd1XHUwMDI2dXRtX2NvbnRlb=
nQ9aW1hZ2VMaW5rIiwibGlua19pZCI6MzQwMDkxNiwicG9zaXRpb24iOjV9/9f2cd72a8b51f4d=
e166d04c203b5e11fc0f72d0330438ccccc105a247c59ca18" style=3D"color: #03a9f4 =
!important; text-decoration: none;"><img width=3D"250" class=3D"center" src=
=3D"https://static.brilliant.org/static/sync/email-images/quiz_emails/geo1/=
hex2.png" alt=3D"picture or diagram" title=3D"picture or diagram" style=3D"=
max-width: 100%; height: auto; line-height: 100%; outline: none; text-decor=
ation: none; -ms-interpolation-mode: bicubic; text-align: center; margin: 0=
 auto; border: 0 none;"/></a></center>
<br style=3D"font-family: &#39;Helvetica&#39;, &#39;Arial&#39;, sans-serif;=
 font-weight: normal; font-size: 15px; line-height: 18px; color: #333;"/>
<a href=3D"https://t.brilliant.org/e/c/eyJlbWFpbF9pZCI6IlJQNG9BUUFCY0tQWF93=
d2dSR2R3SkZzREhBUk4iLCJocmVmIjoiaHR0cHM6Ly9icmlsbGlhbnQub3JnL3ByYWN0aWNlL3R=
yaWFuZ2xlcy1hbmQtaGV4YWdvbnMtMi8_cHJvYmxlbT1iYXNpYy0yZC1nZW9tZXRyeS1wcm9ibG=
VtLTE2MzI5Nlx1MDAyNmNoYXB0ZXI9aW50cm9kdWN0aW9uLXRvLWJhc2ljLTJkLWdlb21ldHJ5X=
HUwMDI2dXRtX3NvdXJjZT1icmlsbGlhbnRcdTAwMjZ1dG1fbWVkaXVtPWVtYWlsXHUwMDI2dXRt=
X2NhbXBhaWduPW5scy1hcDEtcVx1MDAyNnV0bV90ZXJtPWdlbzEtdHJpYW5kaGV4XHUwMDI2YXV=
0b19sb2dpbl9rZXk9bTdXRFpkVGdWZ2xZZU9OOEJhUkN5MmJidFo0UEpQVnJ6VHVPNWtrYVd1XH=
UwMDI2dXRtX2NvbnRlbnQ9cGFuZVRleHRMaW5rIiwibGlua19pZCI6MTkzOTQyODg3LCJwb3Npd=
GlvbiI6Nn0/a3909c77189746e83b9a80adf4b9f063e3cc1afa43a684ab4b598739adcb7bac=
" style=3D"color: #03a9f4 !important; text-decoration: none;"><div class=3D=
"problem-text" style=3D"font-family: &#39;Helvetica&#39;, &#39;Arial&#39;, =
sans-serif; font-weight: normal; font-size: 15px; line-height: 18px; color:=
 #333; margin: 18px 0 0; padding: 0;"><div class=3D"p" style=3D"font-family=
: &#39;Helvetica&#39;, &#39;Arial&#39;, sans-serif; font-weight: normal; fo=
nt-size: 20px; line-height: 28px; color: #333; margin: 10px 0 0; padding: 0=
;">
In <i>Triangles and Hexagons</i>, you=E2=80=99ll learn how complex and beau=
tiful geometry problems can be thought of in terms of triangle pieces.  Onc=
e you know how to break down a problem, the solution will be that much easi=
er to see.=20=20=20=20

<br style=3D"font-family: &#39;Helvetica&#39;, &#39;Arial&#39;, sans-serif;=
 font-weight: normal; font-size: 15px; line-height: 18px; color: #333;"/><b=
r style=3D"font-family: &#39;Helvetica&#39;, &#39;Arial&#39;, sans-serif; f=
ont-weight: normal; font-size: 15px; line-height: 18px; color: #333;"/>

<b>Where we start:</b><br style=3D"font-family: &#39;Helvetica&#39;, &#39;A=
rial&#39;, sans-serif; font-weight: normal; font-size: 15px; line-height: 1=
8px; color: #333;"/><br style=3D"font-family: &#39;Helvetica&#39;, &#39;Ari=
al&#39;, sans-serif; font-weight: normal; font-size: 15px; line-height: 18p=
x; color: #333;"/>
</div></div></a>
<center style=3D"width: 100%; min-width: 0 !important;"><a href=3D"https://=
t.brilliant.org/e/c/eyJlbWFpbF9pZCI6IlJQNG9BUUFCY0tQWF93d2dSR2R3SkZzREhBUk4=
iLCJocmVmIjoiaHR0cHM6Ly9icmlsbGlhbnQub3JnL3ByYWN0aWNlL3RyaWFuZ2xlcy1hbmQtaG=
V4YWdvbnMtMi8_cHJvYmxlbT1iYXNpYy0yZC1nZW9tZXRyeS1wcm9ibGVtLTE2MzI5Nlx1MDAyN=
mNoYXB0ZXI9aW50cm9kdWN0aW9uLXRvLWJhc2ljLTJkLWdlb21ldHJ5XHUwMDI2dXRtX3NvdXJj=
ZT1icmlsbGlhbnRcdTAwMjZ1dG1fbWVkaXVtPWVtYWlsXHUwMDI2dXRtX2NhbXBhaWduPW5scy1=
hcDEtcVx1MDAyNnV0bV90ZXJtPWdlbzEtdHJpYW5kaGV4XHUwMDI2YXV0b19sb2dpbl9rZXk9bT=
dXRFpkVGdWZ2xZZU9OOEJhUkN5MmJidFo0UEpQVnJ6VHVPNWtrYVd1XHUwMDI2dXRtX2NvbnRlb=
nQ9aW1hZ2VMaW5rIiwibGlua19pZCI6MzQwMDkxNiwicG9zaXRpb24iOjd9/da5a777eca91fd2=
62306da914ed2c0098d9184ea78feb1989f5baaef671396d6" style=3D"color: #03a9f4 =
!important; text-decoration: none;"><img width=3D"250" class=3D"center" src=
=3D"https://static.brilliant.org/static/sync/email-images/quiz_emails/geo1/=
hex3.png" alt=3D"picture or diagram" title=3D"picture or diagram" style=3D"=
max-width: 100%; height: auto; line-height: 100%; outline: none; text-decor=
ation: none; -ms-interpolation-mode: bicubic; text-align: center; margin: 0=
 auto; border: 0 none;"/></a></center>
<br style=3D"font-family: &#39;Helvetica&#39;, &#39;Arial&#39;, sans-serif;=
 font-weight: normal; font-size: 15px; line-height: 18px; color: #333;"/>
<a href=3D"https://t.brilliant.org/e/c/eyJlbWFpbF9pZCI6IlJQNG9BUUFCY0tQWF93=
d2dSR2R3SkZzREhBUk4iLCJocmVmIjoiaHR0cHM6Ly9icmlsbGlhbnQub3JnL3ByYWN0aWNlL3R=
yaWFuZ2xlcy1hbmQtaGV4YWdvbnMtMi8_cHJvYmxlbT1iYXNpYy0yZC1nZW9tZXRyeS1wcm9ibG=
VtLTE2MzI5Nlx1MDAyNmNoYXB0ZXI9aW50cm9kdWN0aW9uLXRvLWJhc2ljLTJkLWdlb21ldHJ5X=
HUwMDI2dXRtX3NvdXJjZT1icmlsbGlhbnRcdTAwMjZ1dG1fbWVkaXVtPWVtYWlsXHUwMDI2dXRt=
X2NhbXBhaWduPW5scy1hcDEtcVx1MDAyNnV0bV90ZXJtPWdlbzEtdHJpYW5kaGV4XHUwMDI2YXV=
0b19sb2dpbl9rZXk9bTdXRFpkVGdWZ2xZZU9OOEJhUkN5MmJidFo0UEpQVnJ6VHVPNWtrYVd1XH=
UwMDI2dXRtX2NvbnRlbnQ9cGFuZVRleHRMaW5rIiwibGlua19pZCI6MTkzOTQyODg3LCJwb3Npd=
GlvbiI6OH0/4c3a7aa7c9d1743bce2aa545da0716b886e7c62e89851d0c0c2838d375e23991=
" style=3D"color: #03a9f4 !important; text-decoration: none;"><div class=3D=
"problem-text" style=3D"font-family: &#39;Helvetica&#39;, &#39;Arial&#39;, =
sans-serif; font-weight: normal; font-size: 15px; line-height: 18px; color:=
 #333; margin: 18px 0 0; padding: 0;"><div class=3D"p" style=3D"font-family=
: &#39;Helvetica&#39;, &#39;Arial&#39;, sans-serif; font-weight: normal; fo=
nt-size: 20px; line-height: 28px; color: #333; margin: 10px 0 0; padding: 0=
;">
The figure above is a regular hexagon split up into a triangle, a rhombus, =
and a trapezoid.
<br style=3D"font-family: &#39;Helvetica&#39;, &#39;Arial&#39;, sans-serif;=
 font-weight: normal; font-size: 15px; line-height: 18px; color: #333;"/><b=
r style=3D"font-family: &#39;Helvetica&#39;, &#39;Arial&#39;, sans-serif; f=
ont-weight: normal; font-size: 15px; line-height: 18px; color: #333;"/>
If the area of the blue triangle is 3, what is the area of the orange trape=
zoid?
</div></div></a>
<br style=3D"font-family: &#39;Helvetica&#39;, &#39;Arial&#39;, sans-serif;=
 font-weight: normal; font-size: 15px; line-height: 18px; color: #333;"/><b=
r style=3D"font-family: &#39;Helvetica&#39;, &#39;Arial&#39;, sans-serif; f=
ont-weight: normal; font-size: 15px; line-height: 18px; color: #333;"/>
<center style=3D"width: 100%; min-width: 0 !important;"><ul class=3D"choice=
s" style=3D"list-style-type: none; margin: 0; padding: 0;">
            <li style=3D"list-style-type: none; margin: 0 0 12px; padding: =
0;"><a href=3D"https://t.brilliant.org/e/c/eyJlbWFpbF9pZCI6IlJQNG9BUUFCY0tQ=
WF93d2dSR2R3SkZzREhBUk4iLCJocmVmIjoiaHR0cHM6Ly9icmlsbGlhbnQub3JnL3ByYWN0aWN=
lL3RyaWFuZ2xlcy1hbmQtaGV4YWdvbnMtMi8_cHJvYmxlbT1iYXNpYy0yZC1nZW9tZXRyeS1wcm=
9ibGVtLTE2MzI5Nlx1MDAyNmNoYXB0ZXI9aW50cm9kdWN0aW9uLXRvLWJhc2ljLTJkLWdlb21ld=
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dXRtX2NhbXBhaWduPW5scy1hcDEtcVx1MDAyNnV0bV90ZXJtPWdlbzEtdHJpYW5kaGV4XHUwMDI=
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d1XHUwMDI2dXRtX2NvbnRlbnQ9Y2hvaWNlIiwibGlua19pZCI6MTkzOTQyODk0LCJwb3NpdGlvb=
iI6OX0/f0fe84b9ca769dbe1944ff20577a0d69489784ffabf14d93ce9531647eaab475" st=
yle=3D"color: #fff !important; text-decoration: none; display: inline-block=
; font-weight: bold; font-size: 14px; line-height: 21px; background-color: =
#000; -webkit-border-radius: 12px; -moz-border-radius: 12px; border-radius:=
 12px; border-color: #000; border-style: solid; border-width: 7px 14px;">
                8
            </a>
            <a href=3D"https://t.brilliant.org/e/c/eyJlbWFpbF9pZCI6IlJQNG9B=
UUFCY0tQWF93d2dSR2R3SkZzREhBUk4iLCJocmVmIjoiaHR0cHM6Ly9icmlsbGlhbnQub3JnL3B=
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3NpdGlvbiI6MTB9/fb55a72c2a5f60f107a4f5b309aa33cd75ac6afbacb3cc8091957084b72=
0e561" style=3D"color: #fff !important; text-decoration: none; display: inl=
ine-block; font-weight: bold; font-size: 14px; line-height: 21px; backgroun=
d-color: #000; -webkit-border-radius: 12px; -moz-border-radius: 12px; borde=
r-radius: 12px; border-color: #000; border-style: solid; border-width: 7px =
14px;">
                9
            </a>
            <a href=3D"https://t.brilliant.org/e/c/eyJlbWFpbF9pZCI6IlJQNG9B=
UUFCY0tQWF93d2dSR2R3SkZzREhBUk4iLCJocmVmIjoiaHR0cHM6Ly9icmlsbGlhbnQub3JnL3B=
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3NpdGlvbiI6MTF9/fc8231ab1f8837841e683eb668965e219094a37a762f76158a4360a5c5a=
c5a92" style=3D"color: #fff !important; text-decoration: none; display: inl=
ine-block; font-weight: bold; font-size: 14px; line-height: 21px; backgroun=
d-color: #000; -webkit-border-radius: 12px; -moz-border-radius: 12px; borde=
r-radius: 12px; border-color: #000; border-style: solid; border-width: 7px =
14px;">
                12
            </a>
            <a href=3D"https://t.brilliant.org/e/c/eyJlbWFpbF9pZCI6IlJQNG9B=
UUFCY0tQWF93d2dSR2R3SkZzREhBUk4iLCJocmVmIjoiaHR0cHM6Ly9icmlsbGlhbnQub3JnL3B=
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3NpdGlvbiI6MTJ9/ca0e6b1a7825bfdef417b41f5d495a04af107b3195d5a1ec87f30c92984=
e60f2" style=3D"color: #fff !important; text-decoration: none; display: inl=
ine-block; font-weight: bold; font-size: 14px; line-height: 21px; backgroun=
d-color: #000; -webkit-border-radius: 12px; -moz-border-radius: 12px; borde=
r-radius: 12px; border-color: #000; border-style: solid; border-width: 7px =
14px;">
                18
            </a></li>
=20=20=20=20=20=20=20=20=20=20=20=20
        </ul></center><br style=3D"font-family: &#39;Helvetica&#39;, &#39;A=
rial&#39;, sans-serif; font-weight: normal; font-size: 15px; line-height: 1=
8px; color: #333;"/>

<a href=3D"https://t.brilliant.org/e/c/eyJlbWFpbF9pZCI6IlJQNG9BUUFCY0tQWF93=
d2dSR2R3SkZzREhBUk4iLCJocmVmIjoiaHR0cHM6Ly9icmlsbGlhbnQub3JnL3ByYWN0aWNlL3R=
yaWFuZ2xlcy1hbmQtaGV4YWdvbnMtMi8_cHJvYmxlbT1iYXNpYy0yZC1nZW9tZXRyeS1wcm9ibG=
VtLTE2MzI5Nlx1MDAyNmNoYXB0ZXI9aW50cm9kdWN0aW9uLXRvLWJhc2ljLTJkLWdlb21ldHJ5X=
HUwMDI2dXRtX3NvdXJjZT1icmlsbGlhbnRcdTAwMjZ1dG1fbWVkaXVtPWVtYWlsXHUwMDI2dXRt=
X2NhbXBhaWduPW5scy1hcDEtcVx1MDAyNnV0bV90ZXJtPWdlbzEtdHJpYW5kaGV4XHUwMDI2YXV=
0b19sb2dpbl9rZXk9bTdXRFpkVGdWZ2xZZU9OOEJhUkN5MmJidFo0UEpQVnJ6VHVPNWtrYVd1XH=
UwMDI2dXRtX2NvbnRlbnQ9cGFuZVRleHRMaW5rIiwibGlua19pZCI6MTkzOTQyODg3LCJwb3Npd=
GlvbiI6MTN9/edeaf4c301ae5f13a1fd3c4ea8a677c7716f08bde0b499115669153d225a102=
0" style=3D"color: #03a9f4 !important; text-decoration: none;"><div class=
=3D"problem-text" style=3D"font-family: &#39;Helvetica&#39;, &#39;Arial&#39=
;, sans-serif; font-weight: normal; font-size: 15px; line-height: 18px; col=
or: #333; margin: 18px 0 0; padding: 0;"><div class=3D"p" style=3D"font-fam=
ily: &#39;Helvetica&#39;, &#39;Arial&#39;, sans-serif; font-weight: normal;=
 font-size: 20px; line-height: 28px; color: #333; margin: 10px 0 0; padding=
: 0;">=20=20=20=20=20=20=20=20
<b>Where we end up:</b><br style=3D"font-family: &#39;Helvetica&#39;, &#39;=
Arial&#39;, sans-serif; font-weight: normal; font-size: 15px; line-height: =
18px; color: #333;"/><br style=3D"font-family: &#39;Helvetica&#39;, &#39;Ar=
ial&#39;, sans-serif; font-weight: normal; font-size: 15px; line-height: 18=
px; color: #333;"/>
</div></div></a>
<center style=3D"width: 100%; min-width: 0 !important;"><a href=3D"https://=
t.brilliant.org/e/c/eyJlbWFpbF9pZCI6IlJQNG9BUUFCY0tQWF93d2dSR2R3SkZzREhBUk4=
iLCJocmVmIjoiaHR0cHM6Ly9icmlsbGlhbnQub3JnL3ByYWN0aWNlL3RyaWFuZ2xlcy1hbmQtaG=
V4YWdvbnMtMi8_cHJvYmxlbT1iYXNpYy0yZC1nZW9tZXRyeS1wcm9ibGVtLTE2MzI5Nlx1MDAyN=
mNoYXB0ZXI9aW50cm9kdWN0aW9uLXRvLWJhc2ljLTJkLWdlb21ldHJ5XHUwMDI2dXRtX3NvdXJj=
ZT1icmlsbGlhbnRcdTAwMjZ1dG1fbWVkaXVtPWVtYWlsXHUwMDI2dXRtX2NhbXBhaWduPW5scy1=
hcDEtcVx1MDAyNnV0bV90ZXJtPWdlbzEtdHJpYW5kaGV4XHUwMDI2YXV0b19sb2dpbl9rZXk9bT=
dXRFpkVGdWZ2xZZU9OOEJhUkN5MmJidFo0UEpQVnJ6VHVPNWtrYVd1XHUwMDI2dXRtX2NvbnRlb=
nQ9aW1hZ2VMaW5rIiwibGlua19pZCI6MzQwMDkxNiwicG9zaXRpb24iOjE0fQ/115dd9a869872=
d8ee050607744c5db7e1eb7f7575adcd251ef356bb068d53c7b" style=3D"color: #03a9f=
4 !important; text-decoration: none;"><img width=3D"250" class=3D"center" s=
rc=3D"https://static.brilliant.org/static/sync/email-images/quiz_emails/geo=
1/hex4.png" alt=3D"picture or diagram" title=3D"picture or diagram" style=
=3D"max-width: 100%; height: auto; line-height: 100%; outline: none; text-d=
ecoration: none; -ms-interpolation-mode: bicubic; text-align: center; margi=
n: 0 auto; border: 0 none;"/></a></center>

<a href=3D"https://t.brilliant.org/e/c/eyJlbWFpbF9pZCI6IlJQNG9BUUFCY0tQWF93=
d2dSR2R3SkZzREhBUk4iLCJocmVmIjoiaHR0cHM6Ly9icmlsbGlhbnQub3JnL3ByYWN0aWNlL3R=
yaWFuZ2xlcy1hbmQtaGV4YWdvbnMtMi8_cHJvYmxlbT1iYXNpYy0yZC1nZW9tZXRyeS1wcm9ibG=
VtLTE2MzI5Nlx1MDAyNmNoYXB0ZXI9aW50cm9kdWN0aW9uLXRvLWJhc2ljLTJkLWdlb21ldHJ5X=
HUwMDI2dXRtX3NvdXJjZT1icmlsbGlhbnRcdTAwMjZ1dG1fbWVkaXVtPWVtYWlsXHUwMDI2dXRt=
X2NhbXBhaWduPW5scy1hcDEtcVx1MDAyNnV0bV90ZXJtPWdlbzEtdHJpYW5kaGV4XHUwMDI2YXV=
0b19sb2dpbl9rZXk9bTdXRFpkVGdWZ2xZZU9OOEJhUkN5MmJidFo0UEpQVnJ6VHVPNWtrYVd1XH=
UwMDI2dXRtX2NvbnRlbnQ9cGFuZVRleHRMaW5rIiwibGlua19pZCI6MTkzOTQyODg3LCJwb3Npd=
GlvbiI6MTV9/dcbc4f14b063a235b17361cb4d9229701d6601932d310a4e09e80b6c1e67d0b=
4" style=3D"color: #03a9f4 !important; text-decoration: none;"><div class=
=3D"problem-text" style=3D"font-family: &#39;Helvetica&#39;, &#39;Arial&#39=
;, sans-serif; font-weight: normal; font-size: 15px; line-height: 18px; col=
or: #333; margin: 18px 0 0; padding: 0;"><div class=3D"p" style=3D"font-fam=
ily: &#39;Helvetica&#39;, &#39;Arial&#39;, sans-serif; font-weight: normal;=
 font-size: 20px; line-height: 28px; color: #333; margin: 10px 0 0; padding=
: 0;">=20=20=20=20=20=20=20=20
An equilateral triangle is placed in a regular hexagon so that its vertices=
 lie in the middle of the hexagon&#39;s sides.=20
<br style=3D"font-family: &#39;Helvetica&#39;, &#39;Arial&#39;, sans-serif;=
 font-weight: normal; font-size: 15px; line-height: 18px; color: #333;"/><b=
r style=3D"font-family: &#39;Helvetica&#39;, &#39;Arial&#39;, sans-serif; f=
ont-weight: normal; font-size: 15px; line-height: 18px; color: #333;"/>
Which is greater, the orange area or the blue area?
<br style=3D"font-family: &#39;Helvetica&#39;, &#39;Arial&#39;, sans-serif;=
 font-weight: normal; font-size: 15px; line-height: 18px; color: #333;"/><b=
r style=3D"font-family: &#39;Helvetica&#39;, &#39;Arial&#39;, sans-serif; f=
ont-weight: normal; font-size: 15px; line-height: 18px; color: #333;"/>
</div></div></a>
<ul class=3D"choices" style=3D"list-style-type: none; margin: 0; padding: 0=
;">
            <li style=3D"list-style-type: none; margin: 0 0 12px; padding: =
0;"><a href=3D"https://t.brilliant.org/e/c/eyJlbWFpbF9pZCI6IlJQNG9BUUFCY0tQ=
WF93d2dSR2R3SkZzREhBUk4iLCJocmVmIjoiaHR0cHM6Ly9icmlsbGlhbnQub3JnL3ByYWN0aWN=
lL3RyaWFuZ2xlcy1hbmQtaGV4YWdvbnMtMi8_cHJvYmxlbT1iYXNpYy0yZC1nZW9tZXRyeS1wcm=
9ibGVtLTE2MzI5Nlx1MDAyNmNoYXB0ZXI9aW50cm9kdWN0aW9uLXRvLWJhc2ljLTJkLWdlb21ld=
HJ5XHUwMDI2dXRtX3NvdXJjZT1icmlsbGlhbnRcdTAwMjZ1dG1fbWVkaXVtPWVtYWlsXHUwMDI2=
dXRtX2NhbXBhaWduPW5scy1hcDEtcVx1MDAyNnV0bV90ZXJtPWdlbzEtdHJpYW5kaGV4XHUwMDI=
2YXV0b19sb2dpbl9rZXk9bTdXRFpkVGdWZ2xZZU9OOEJhUkN5MmJidFo0UEpQVnJ6VHVPNWtrYV=
d1XHUwMDI2dXRtX2NvbnRlbnQ9Y2hvaWNlIiwibGlua19pZCI6MTkzOTQyODk0LCJwb3NpdGlvb=
iI6MTZ9/2f6fc31e6eea04df8987a065238e56fbf512843721b895c19c9084d0d6d0afaa" s=
tyle=3D"color: #fff !important; text-decoration: none; display: inline-bloc=
k; font-weight: bold; font-size: 14px; line-height: 21px; background-color:=
 #000; -webkit-border-radius: 12px; -moz-border-radius: 12px; border-radius=
: 12px; border-color: #000; border-style: solid; border-width: 7px 14px;">
                The orange area
            </a></li>
            <li style=3D"list-style-type: none; margin: 0 0 12px; padding: =
0;"><a href=3D"https://t.brilliant.org/e/c/eyJlbWFpbF9pZCI6IlJQNG9BUUFCY0tQ=
WF93d2dSR2R3SkZzREhBUk4iLCJocmVmIjoiaHR0cHM6Ly9icmlsbGlhbnQub3JnL3ByYWN0aWN=
lL3RyaWFuZ2xlcy1hbmQtaGV4YWdvbnMtMi8_cHJvYmxlbT1iYXNpYy0yZC1nZW9tZXRyeS1wcm=
9ibGVtLTE2MzI5Nlx1MDAyNmNoYXB0ZXI9aW50cm9kdWN0aW9uLXRvLWJhc2ljLTJkLWdlb21ld=
HJ5XHUwMDI2dXRtX3NvdXJjZT1icmlsbGlhbnRcdTAwMjZ1dG1fbWVkaXVtPWVtYWlsXHUwMDI2=
dXRtX2NhbXBhaWduPW5scy1hcDEtcVx1MDAyNnV0bV90ZXJtPWdlbzEtdHJpYW5kaGV4XHUwMDI=
2YXV0b19sb2dpbl9rZXk9bTdXRFpkVGdWZ2xZZU9OOEJhUkN5MmJidFo0UEpQVnJ6VHVPNWtrYV=
d1XHUwMDI2dXRtX2NvbnRlbnQ9Y2hvaWNlIiwibGlua19pZCI6MTkzOTQyODk0LCJwb3NpdGlvb=
iI6MTd9/42e2bc77b4412a0d1dee874b5f62d3752eba5940fca561f73f4ef55ca85e5e56" s=
tyle=3D"color: #fff !important; text-decoration: none; display: inline-bloc=
k; font-weight: bold; font-size: 14px; line-height: 21px; background-color:=
 #000; -webkit-border-radius: 12px; -moz-border-radius: 12px; border-radius=
: 12px; border-color: #000; border-style: solid; border-width: 7px 14px;">
                The blue area
            </a></li>
            <li style=3D"list-style-type: none; margin: 0 0 12px; padding: =
0;"><a href=3D"https://t.brilliant.org/e/c/eyJlbWFpbF9pZCI6IlJQNG9BUUFCY0tQ=
WF93d2dSR2R3SkZzREhBUk4iLCJocmVmIjoiaHR0cHM6Ly9icmlsbGlhbnQub3JnL3ByYWN0aWN=
lL3RyaWFuZ2xlcy1hbmQtaGV4YWdvbnMtMi8_cHJvYmxlbT1iYXNpYy0yZC1nZW9tZXRyeS1wcm=
9ibGVtLTE2MzI5Nlx1MDAyNmNoYXB0ZXI9aW50cm9kdWN0aW9uLXRvLWJhc2ljLTJkLWdlb21ld=
HJ5XHUwMDI2dXRtX3NvdXJjZT1icmlsbGlhbnRcdTAwMjZ1dG1fbWVkaXVtPWVtYWlsXHUwMDI2=
dXRtX2NhbXBhaWduPW5scy1hcDEtcVx1MDAyNnV0bV90ZXJtPWdlbzEtdHJpYW5kaGV4XHUwMDI=
2YXV0b19sb2dpbl9rZXk9bTdXRFpkVGdWZ2xZZU9OOEJhUkN5MmJidFo0UEpQVnJ6VHVPNWtrYV=
d1XHUwMDI2dXRtX2NvbnRlbnQ9Y2hvaWNlIiwibGlua19pZCI6MTkzOTQyODk0LCJwb3NpdGlvb=
iI6MTh9/228e91340292d82ac91ed1bed4deb28e83c3536eb0d161e5cb446580c7e36128" s=
tyle=3D"color: #fff !important; text-decoration: none; display: inline-bloc=
k; font-weight: bold; font-size: 14px; line-height: 21px; background-color:=
 #000; -webkit-border-radius: 12px; -moz-border-radius: 12px; border-radius=
: 12px; border-color: #000; border-style: solid; border-width: 7px 14px;">
                They have the same area
            </a></li>
        </ul>

<br style=3D"font-family: &#39;Helvetica&#39;, &#39;Arial&#39;, sans-serif;=
 font-weight: normal; font-size: 15px; line-height: 18px; color: #333;"/><b=
r style=3D"font-family: &#39;Helvetica&#39;, &#39;Arial&#39;, sans-serif; f=
ont-weight: normal; font-size: 15px; line-height: 18px; color: #333;"/>

=20=20=20=20=20=20=20=20
        <table class=3D"inner" style=3D"border-collapse: collapse !importan=
t; max-width: 100%; mso-table-lspace: 0pt; mso-table-rspace: 0pt; border-sp=
acing: 0; vertical-align: top; text-align: left; width: 306px; position: re=
lative; margin: 0 auto; padding: 0;"><tbody><tr style=3D"vertical-align: to=
p; text-align: left; margin: 0; padding: 0;" align=3D"left"><td align=3D"ce=
nter" class=3D"center" style=3D"border-collapse: collapse !important; verti=
cal-align: top; text-align: center; font-family: &#39;Helvetica&#39;, &#39;=
Arial&#39;, sans-serif; font-weight: normal; font-size: 15px; line-height: =
18px; color: #333; margin: 0; padding: 0;" valign=3D"top"><center style=3D"=
width: 100%; min-width: 0 !important;">
          <a href=3D"https://t.brilliant.org/e/c/eyJlbWFpbF9pZCI6IlJQNG9BUU=
FCY0tQWF93d2dSR2R3SkZzREhBUk4iLCJocmVmIjoiaHR0cHM6Ly9icmlsbGlhbnQub3JnL3ByY=
WN0aWNlL3RyaWFuZ2xlcy1hbmQtaGV4YWdvbnMtMi8_cHJvYmxlbT1iYXNpYy0yZC1nZW9tZXRy=
eS1wcm9ibGVtLTE2MzI5Nlx1MDAyNmNoYXB0ZXI9aW50cm9kdWN0aW9uLXRvLWJhc2ljLTJkLWd=
lb21ldHJ5XHUwMDI2dXRtX3NvdXJjZT1icmlsbGlhbnRcdTAwMjZ1dG1fbWVkaXVtPWVtYWlsXH=
UwMDI2dXRtX2NhbXBhaWduPW5scy1hcDEtcVx1MDAyNnV0bV90ZXJtPWdlbzEtdHJpYW5kaGV4X=
HUwMDI2YXV0b19sb2dpbl9rZXk9bTdXRFpkVGdWZ2xZZU9OOEJhUkN5MmJidFo0UEpQVnJ6VHVP=
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pdGlvbiI6MTl9/6db64e437e552d6f6744d6205d9bcc54e3fb9673466f08a67a991de898143=
e67" class=3D"button-black2" style=3D"color: #FFFFFF !important; text-decor=
ation: none; display: inline-block; font-size: 15px; line-height: 20px; bac=
kground-color: #000000; font-family: Soleil,Roboto,Helvetica,Arial,sans-ser=
if; text-transform: uppercase; padding: 14px 60px; border: 0px solid #000;"=
>Start exploring</a>
        </center></td></tr></tbody></table>

    </td></tr></tbody></table>
    </center></td></tr></tbody></table>
=20=20=20=20

=20=20=20=20
    <table class=3D"outer" style=3D"border-collapse: collapse !important; m=
ax-width: 100%; mso-table-lspace: 0pt; mso-table-rspace: 0pt; border-spacin=
g: 0; vertical-align: top; text-align: left; width: 448px; margin: 0 auto; =
padding: 0;"><tbody><tr style=3D"vertical-align: top; text-align: left; mar=
gin: 0; padding: 0;" align=3D"left"><td align=3D"center" style=3D"border-to=
p-width: 1px; border-top-color: #F0F0F0; border-top-style: solid; border-co=
llapse: collapse !important; vertical-align: top; text-align: center; font-=
family: &#39;Helvetica&#39;, &#39;Arial&#39;, sans-serif; font-weight: norm=
al; font-size: 15px; line-height: 18px; color: #333; width: 448px; backgrou=
nd-color: #fff; margin: 0; padding: 0;" class=3D"content-wrapper center" bg=
color=3D"#fff" valign=3D"top"><center style=3D"width: 100%; min-width: 0 !i=
mportant;">
        <table class=3D"inner" style=3D"border-collapse: collapse !importan=
t; max-width: 100%; mso-table-lspace: 0pt; mso-table-rspace: 0pt; border-sp=
acing: 0; vertical-align: top; text-align: left; width: 306px; position: re=
lative; margin: 0 auto; padding: 0;"><tbody><tr style=3D"vertical-align: to=
p; text-align: left; margin: 0; padding: 0;" align=3D"left"><td class=3D"co=
ntent" style=3D"border-collapse: collapse !important; vertical-align: top; =
text-align: left; font-family: &#39;Helvetica&#39;, &#39;Arial&#39;, sans-s=
erif; font-weight: normal; font-size: 15px; line-height: 18px; color: #333;=
 position: relative; margin: 0; padding: 20px 0 28px;" align=3D"left" valig=
n=3D"top">
            <table class=3D"mobile-app-badges" style=3D"border-collapse: co=
llapse !important; max-width: 100%; mso-table-lspace: 0pt; mso-table-rspace=
: 0pt; border-spacing: 0; vertical-align: top; text-align: left; width: 100=
%; min-width: 100%; margin: 0; padding: 0;"><tbody><tr style=3D"vertical-al=
ign: top; text-align: left; margin: 0; padding: 0;" align=3D"left">
                <td class=3D"app-store" style=3D"border-collapse: collapse =
!important; vertical-align: top; text-align: right; font-family: &#39;Helve=
tica&#39;, &#39;Arial&#39;, sans-serif; font-weight: normal; font-size: 15p=
x; line-height: 10px; color: #333; width: 47%; margin: 0; padding: 8px 0 0;=
" align=3D"right" valign=3D"top">
                    <a href=3D"https://t.brilliant.org/e/c/eyJlbWFpbF9pZCI6=
IlJQNG9BUUFCY0tQWF93d2dSR2R3SkZzREhBUk4iLCJocmVmIjoiaHR0cHM6Ly9pdHVuZXMuYXB=
wbGUuY29tL3VzL2FwcC9hcHBsZS1zdG9yZS9pZDkxMzMzNTI1Mj9wdD0xMDUwOTU4MDNcdTAwMj=
ZjdD1lbWFpbF9mb290ZXJcdTAwMjZtdD04IiwibGlua19pZCI6MTEzNDQ5MzMsInBvc2l0aW9uI=
joyMH0/f0baaf4e6cf8a08b2086ba2e7fb4f7edb9e97895da5ae00d686282909f6a86f1" st=
yle=3D"color: #03a9f4 !important; text-decoration: none;">
                        <img width=3D"143" alt=3D"Brilliant" src=3D"https:/=
/static.brilliant.org/static/manual/app-store.png" height=3D"42" border=3D"=
0" style=3D"max-width: 100%; height: auto; line-height: 100%; outline: none=
; text-decoration: none; -ms-interpolation-mode: bicubic; border: 0 none;"/>
                    </a>
                </td>
                <td class=3D"spacer" style=3D"border-collapse: collapse !im=
portant; vertical-align: top; text-align: left; font-family: &#39;Helvetica=
&#39;, &#39;Arial&#39;, sans-serif; font-weight: normal; font-size: 15px; l=
ine-height: 10px; color: #333; width: 6%; margin: 0; padding: 8px 0 0;" ali=
gn=3D"left" valign=3D"top"></td>
                <td class=3D"google-play" style=3D"border-collapse: collaps=
e !important; vertical-align: top; text-align: left; font-family: &#39;Helv=
etica&#39;, &#39;Arial&#39;, sans-serif; font-weight: normal; font-size: 15=
px; line-height: 10px; color: #333; width: 47%; margin: 0; padding: 8px 0 0=
;" align=3D"left" valign=3D"top">
                    <a href=3D"https://t.brilliant.org/e/c/eyJlbWFpbF9pZCI6=
IlJQNG9BUUFCY0tQWF93d2dSR2R3SkZzREhBUk4iLCJocmVmIjoiaHR0cHM6Ly9wbGF5Lmdvb2d=
sZS5jb20vc3RvcmUvYXBwcy9kZXRhaWxzP2lkPW9yZy5icmlsbGlhbnQuYW5kcm9pZFx1MDAyNn=
JlZmVycmVyPXV0bV9zb3VyY2UlM0RicmlsbGlhbnQlMjZ1dG1fbWVkaXVtJTNEZW1haWwlMjYiL=
CJsaW5rX2lkIjoxOTM5NDE4NTEsInBvc2l0aW9uIjoyMX0/b501c1cf624b3b6b355b3fa6ccb7=
0376978cdf3000ca04f84cabfa2d4d040e0a" style=3D"color: #03a9f4 !important; t=
ext-decoration: none;">
                        <img width=3D"142" alt=3D"Brilliant" src=3D"https:/=
/static.brilliant.org/static/manual/google-play.png" height=3D"42" border=
=3D"0" style=3D"max-width: 100%; height: auto; line-height: 100%; outline: =
none; text-decoration: none; -ms-interpolation-mode: bicubic; border: 0 non=
e;"/>
                    </a>
                </td>
            </tr></tbody></table>

        </td></tr></tbody></table><!--// inner -->
    </center></td></tr></tbody></table><!--// content -->
=20=20=20=20


=20=20=20=20
    <table class=3D"outer" style=3D"border-collapse: collapse !important; m=
ax-width: 100%; mso-table-lspace: 0pt; mso-table-rspace: 0pt; border-spacin=
g: 0; vertical-align: top; text-align: left; width: 448px; margin: 0 auto; =
padding: 0;"><tbody><tr style=3D"vertical-align: top; text-align: left; mar=
gin: 0; padding: 0;" align=3D"left"><td align=3D"center" class=3D"center" s=
tyle=3D"border-collapse: collapse !important; vertical-align: top; text-ali=
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