{"status": "success", "data": {"description_md": "The points $A, B$ and $C$ lie on the surface of a sphere with center $O$ and radius 20. It is given that $AB=13, BC=14, CA=15,$ and that the distance from $O$ to triangle $ABC$ is $\\frac{m\\sqrt{n}}k,$ where $m, n,$ and $k$ are positive integers, $m$ and $k$ are relatively prime, and $n$ is not divisible by the square of any prime. Find $m+n+k.$\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": "

The points A, B and C lie on the surface of a sphere with center O and radius 20. It is given that AB=13, BC=14, CA=15, and that the distance from O to triangle ABC is \\frac{m\\sqrt{n}}k, where m, n, and k are positive integers, m and k are relatively prime, and n is not divisible by the square of any prime. Find m+n+k.

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": "2000 AIME II Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/00_aime_II_p13", "prev": "/problem/00_aime_II_p11"}}