{"status": "success", "data": {"description_md": "In the diagram below, angle $ABC$ is a right angle. Point $D$ is on $\\overline{BC}$, and $\\overline{AD}$ bisects angle $CAB$. Points $E$ and $F$ are on $\\overline{AB}$ and $\\overline{AC}$, respectively, so that $AE=3$ and $AF=10.$ Given that $EB=9$ and $FC=27$, find the integer closest to the area of quadrilateral $DCFG.$<br><br> <img src=\"https://latex.artofproblemsolving.com/6/2/f/62f5e635448a90e26c3d9d976a6380b30ca47d99.png\" width=\"500\">\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full 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 the diagram below, angle <span class=\"katex--inline\">ABC</span> is a right angle. Point <span class=\"katex--inline\">D</span> is on <span class=\"katex--inline\">\\overline{BC}</span>, and <span class=\"katex--inline\">\\overline{AD}</span> bisects angle <span class=\"katex--inline\">CAB</span>. Points <span class=\"katex--inline\">E</span> and <span class=\"katex--inline\">F</span> are on <span class=\"katex--inline\">\\overline{AB}</span> and <span class=\"katex--inline\">\\overline{AC}</span>, respectively, so that <span class=\"katex--inline\">AE=3</span> and <span class=\"katex--inline\">AF=10.</span> Given that <span class=\"katex--inline\">EB=9</span> and <span class=\"katex--inline\">FC=27</span>, find the integer closest to the area of quadrilateral <span class=\"katex--inline\">DCFG.</span><br/><br/> <img src=\"https://latex.artofproblemsolving.com/6/2/f/62f5e635448a90e26c3d9d976a6380b30ca47d99.png\" width=\"500\"/></p>&#10;<hr/>&#10;<p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. 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": 5, "problem_name": "2002 AIME I Problem 10", "can_next": true, "can_prev": true, "nxt": "/problem/02_aime_I_p11", "prev": "/problem/02_aime_I_p09"}}