{"status": "success", "data": {"description_md": "Triangle $ABC$ is inscribed in circle $\\omega$ with $AB = 5$, $BC = 7$, and $AC = 3$. The bisector of angle $A$ meets side $BC$ at $D$ and circle $\\omega$ at a second point $E$. Let $\\gamma$ be the circle with diameter $DE$. Circles $\\omega$ and $\\gamma$ meet at $E$ and a second point $F$. Then $AF^2 = \\frac mn$, 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": "

Triangle ABC is inscribed in circle \\omega with AB = 5, BC = 7, and AC = 3. The bisector of angle A meets side BC at D and circle \\omega at a second point E. Let \\gamma be the circle with diameter DE. Circles \\omega and \\gamma meet at E and a second point F. Then AF^2 = \\frac mn, 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": 6, "problem_name": "2012 AIME II Problem 15", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/12_aime_II_p14"}}