{"status": "success", "data": {"description_md": "Given a point $P$ on a triangular piece of paper $ABC,$ consider the creases that are formed in the paper when $A, B,$ and $C$ are folded onto $P.$ Let us call $P$ a fold point of $\\triangle ABC$ if these creases, which number three unless $P$ is one of the vertices, do not intersect. Suppose that $AB=36, AC=72,$ and $\\angle B=90^\\circ.$ Then the area of the set of all fold points of $\\triangle ABC$ can be written in the form $q\\pi-r\\sqrt{s},$ where $q, r,$ and $s$ are positive integers and $s$ is not divisible by the square of any prime. What is $q+r+s$?\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": "

Given a point P on a triangular piece of paper ABC, consider the creases that are formed in the paper when A, B, and C are folded onto P. Let us call P a fold point of \\triangle ABC if these creases, which number three unless P is one of the vertices, do not intersect. Suppose that AB=36, AC=72, and \\angle B=90^\\circ. Then the area of the set of all fold points of \\triangle ABC can be written in the form q\\pi-r\\sqrt{s}, where q, r, and s are positive integers and s is not divisible by the square of any prime. What is q+r+s?

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": 6, "problem_name": "1994 AIME Problem 15", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/94_aime_p14"}}