{"status": "success", "data": {"description_md": "In triangle $ ABC$, $ AB = AC = 100$, and $ BC = 56$. Circle $ P$ has radius $ 16$ and is tangent to $ \\overline{AC}$ and $ \\overline{BC}$. Circle $ Q$ is externally tangent to $ P$ and is tangent to $ \\overline{AB}$ and $ \\overline{BC}$. No point of circle $ Q$ lies outside of $ \\triangle ABC$. The radius of circle $ Q$ can be expressed in the form $ m - n\\sqrt {k}$, where $ m$, $ n$, and $ k$ are positive integers and $ k$ is the product of distinct primes. Find $ m + nk$.\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$, $ AB = AC = 100$, and $ BC = 56$. Circle $ P$ has radius $ 16$ and is tangent to $ \\overline{AC}$ and $ \\overline{BC}$. Circle $ Q$ is externally tangent to $ P$ and is tangent to $ \\overline{AB}$ and $ \\overline{BC}$. No point of circle $ Q$ lies outside of $ \\triangle ABC$. The radius of circle $ Q$ can be expressed in the form $ m - n\\sqrt {k}$, where $ m$, $ n$, and $ k$ are positive integers and $ k$ is the product of distinct primes. Find $ m + nk$.</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": 5, "problem_name": "2008 AIME II Problem 11", "can_next": true, "can_prev": true, "nxt": "/problem/08_aime_II_p12", "prev": "/problem/08_aime_II_p10"}}