{"status": "success", "data": {"description_md": "In acute triangle $ABC$ points $P$ and $Q$ are the feet of the perpendiculars from $C$ to $\\overline{AB}$ and from $B$ to $\\overline{AC}$, respectively. Line $PQ$ intersects the circumcircle of $\\triangle ABC$ in two distinct points, $X$ and $Y$. Suppose $XP=10$, $PQ=25$, and $QY=15$. The value of $AB\\cdot AC$ can be written in the form $m\\sqrt n$ where $m$ and $n$ are positive integers, and $n$ is not divisible by the square of any prime. Find $m+n$.\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 acute triangle ABC points P and Q are the feet of the perpendiculars from C to \\overline{AB} and from B to \\overline{AC}, respectively. Line PQ intersects the circumcircle of \\triangle ABC in two distinct points, X and Y. Suppose XP=10, PQ=25, and QY=15. The value of AB\\cdot AC can be written in the form m\\sqrt n where m and n are positive integers, and n is not divisible by the square of any prime. Find m+n.

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": "2019 AIME II Problem 15", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/19_aime_II_p14"}}