{"status": "success", "data": {"description_md": "In rectangle $ABCD, AB=5$ and $BC=3$. Points $F$ and $G$ are on $\\overline{CD}$ so that $DF=1$ and $GC=2$. Lines $AF$ and $BG$ intersect at $E$. Find the area of $\\triangle AEB$.\n<a href=\"https://imgbb.com/\"><img src=\"https://i.ibb.co/xY72cPR/image-2024-07-29-210042560.png\" alt=\"image-2024-07-29-210042560\" border=\"0\"></a>\n\n\n$\\text {(A) } 10 \\qquad \\text {(B) } \\frac{21}{2} \\qquad \\text {(C) } 12 \\qquad \\text {(D) } \\frac{25}{2} \\qquad \\text {(E) } 15$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>In rectangle <span class=\"katex--inline\">ABCD, AB=5</span> and <span class=\"katex--inline\">BC=3</span>. Points <span class=\"katex--inline\">F</span> and <span class=\"katex--inline\">G</span> are on <span class=\"katex--inline\">\\overline{CD}</span> so that <span class=\"katex--inline\">DF=1</span> and <span class=\"katex--inline\">GC=2</span>. Lines <span class=\"katex--inline\">AF</span> and <span class=\"katex--inline\">BG</span> intersect at <span class=\"katex--inline\">E</span>. Find the area of <span class=\"katex--inline\">\\triangle AEB</span>.<br/>&#10;<a href=\"https://imgbb.com/\"><img src=\"https://i.ibb.co/xY72cPR/image-2024-07-29-210042560.png\" alt=\"image-2024-07-29-210042560\" border=\"0\"/></a></p>&#10;<p><span class=\"katex--inline\">\\text {(A) } 10 \\qquad \\text {(B) } \\frac{21}{2} \\qquad \\text {(C) } 12 \\qquad \\text {(D) } \\frac{25}{2} \\qquad \\text {(E) } 15</span></p>&#10;<hr/>&#10;<p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2003 AMC 12B Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/03_amc12B_p15", "prev": "/problem/03_amc12B_p13"}}