{"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 $ \\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$.</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": "2010 AIME I Problem 15", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/10_aime_I_p14"}}