{"status": "success", "data": {"description_md": "In triangle $ABC$, $AB=13$, $BC=15$, and $CA=14$. Point $D$ is on $\\overline{BC}$ with $CD=6.$ Point $E$ is on $\\overline{BC}$ such that $\\angle BAE\\cong \\angle CAD.$ Given that $BE=\\frac pq$ where $p$ and $q$ are relatively prime positive integers, find $q.$\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 triangle <span class=\"katex--inline\">ABC</span>, <span class=\"katex--inline\">AB=13</span>, <span class=\"katex--inline\">BC=15</span>, and <span class=\"katex--inline\">CA=14</span>. Point <span class=\"katex--inline\">D</span> is on <span class=\"katex--inline\">\\overline{BC}</span> with <span class=\"katex--inline\">CD=6.</span> Point <span class=\"katex--inline\">E</span> is on <span class=\"katex--inline\">\\overline{BC}</span> such that <span class=\"katex--inline\">\\angle BAE\\cong \\angle CAD.</span> Given that <span class=\"katex--inline\">BE=\\frac pq</span> where <span class=\"katex--inline\">p</span> and <span class=\"katex--inline\">q</span> are relatively prime positive integers, find <span class=\"katex--inline\">q.</span></p>&#10;<hr><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>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 6, "problem_name": "2005 AIME II Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/05_aime_II_p15", "prev": "/problem/05_aime_II_p13"}}