{"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 $\\triangle AEB$.<br>[[File:Problem_14.png]]\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/>[[File:Problem_14.png]]</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><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>", "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"}}