{"status": "success", "data": {"description_md": "Triangle $ABC$ has side lengths $AB=7$, $BC=8$ and $CA=9.$ Circle $\\omega_1$ passes through $B$ and is tangent to line $AC$ at $A.$ Circle $\\omega_2$ passes through $C$ and is tangent to line $AB$ at $A.$ Let $K$ be the intersection of circles $\\omega_1$ and $\\omega_2$ not equal to $A.$ Then $AK=\\tfrac{m}{n},$ 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": "

Triangle ABC has side lengths AB=7, BC=8 and CA=9. Circle \\omega_1 passes through B and is tangent to line AC at A. Circle \\omega_2 passes through C and is tangent to line AB at A. Let K be the intersection of circles \\omega_1 and \\omega_2 not equal to A. Then AK=\\tfrac{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": "2019 AIME II Problem 11", "can_next": true, "can_prev": true, "nxt": "/problem/19_aime_II_p12", "prev": "/problem/19_aime_II_p10"}}