{"status": "success", "data": {"description_md": "Let $ABC$ be an acute triangle with circumcircle $\\omega$ and orthocenter $H$. Suppose the tangent to the circumcircle of $\\triangle HBC$ at $H$ intersects $\\omega$ at points $X$ and $Y$ with $HA=3$, $HX=2$, $HY=6$. The area of $\\triangle ABC$ can be written as $m\\sqrt n$, 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": "

Let ABC be an acute triangle with circumcircle \\omega and orthocenter H. Suppose the tangent to the circumcircle of \\triangle HBC at H intersects \\omega at points X and Y with HA=3, HX=2, HY=6. The area of \\triangle ABC can be written as 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": "2020 AIME I Problem 15", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/20_aime_I_p14"}}