2021 AIME II Problem 14

Let \Delta ABC be an acute triangle with circumcenter O and centroid G. Let X be the intersection of the line tangent to the circumcircle of \Delta 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.