{"status": "success", "data": {"description_md": "In $\\triangle{ABC}$ with $AB = 12$, $BC = 13$, and $AC = 15$, let $M$ be a point on $\\overline{AC}$ such that the incircles of $\\triangle{ABM}$ and $\\triangle{BCM}$ have equal radii. Let $p$ and $q$ be positive relatively prime integers such that $\\tfrac{AM}{CM} = \\tfrac{p}{q}$. Find $p + q$.\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 <span class=\"katex--inline\">\\triangle{ABC}</span> with <span class=\"katex--inline\">AB = 12</span>, <span class=\"katex--inline\">BC = 13</span>, and <span class=\"katex--inline\">AC = 15</span>, let <span class=\"katex--inline\">M</span> be a point on <span class=\"katex--inline\">\\overline{AC}</span> such that the incircles of <span class=\"katex--inline\">\\triangle{ABM}</span> and <span class=\"katex--inline\">\\triangle{BCM}</span> have equal radii. Let <span class=\"katex--inline\">p</span> and <span class=\"katex--inline\">q</span> be positive relatively prime integers such that <span class=\"katex--inline\">\\tfrac{AM}{CM} = \\tfrac{p}{q}</span>. Find <span class=\"katex--inline\">p + q</span>.</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": 6, "problem_name": "2010 AIME I Problem 15", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/10_aime_I_p14"}}