{"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": "

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.

Leading zeroes must be inputted, so if your answer is 34, then input 034. Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "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"}}