{"status": "success", "data": {"description_md": "Let $\\triangle ABC$ have side lengths $AB = 5, BC = 9,$ and $CA = 10.$ The tangents to the circumcircle of $\\triangle ABC$ at $B$ and $C$ intersect at point $D,$ and $\\overline{AD}$ intersects the circumcircle at $P \\ne A.$ The length of $\\overline{AP}$ is equal to $\\frac{m}{n},$ where $m$ and $n$ are relatively prime positive integers. 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 \\triangle ABC have side lengths AB = 5, BC = 9, and CA = 10. The tangents to the circumcircle of \\triangle ABC at B and C intersect at point D, and \\overline{AD} intersects the circumcircle at P \\ne A. The length of \\overline{AP} is equal to \\frac{m}{n}, where m and n are relatively prime positive integers. 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": 5, "problem_name": "2024 AIME I Problem 10", "can_next": true, "can_prev": true, "nxt": "/problem/24_aime_I_p11", "prev": "/problem/24_aime_I_p09"}}