{"status": "success", "data": {"description_md": "Let $\\triangle ABC$ be an acute triangle with circumcenter $O$ and centroid $G$. Let $X$ be the intersection of the line tangent to the circumcircle of $\\triangle ABC$ at $A$ and the line perpendicular to $GO$ at $G$. Let $Y$ be the intersection of lines $XG$ and $BC$. Given that the measures of $\\angle ABC, \\angle BCA, $ and $\\angle XOY$ are in the ratio $13 : 2 : 17, $ the degree measure of $\\angle BAC$ can be written as $\\frac{m}{n},$ where $m$ and $n$ are relatively prime positive integers. Find $m+n$.
$\\includegraphics[width=216, height=227, totalheight=227]{https://latex.artofproblemsolving.com/8/3/5/835aac93eabd97239b45d756761088c6e02b582e.png}$\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 be an acute triangle with circumcenter O and centroid G. Let X be the intersection of the line tangent to the circumcircle of \\triangle ABC at A and the line perpendicular to GO at G. Let Y be the intersection of lines XG and BC. Given that the measures of $\\angle ABC, \\angle BCA, $ and \\angle XOY are in the ratio $13 : 2 : 17, $ the degree measure of \\angle BAC can be written as \\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": 6, "problem_name": "2021 AIME II Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/21_aime_II_p15", "prev": "/problem/21_aime_II_p13"}}