2019 AIME II Problem 15

In acute triangle ABC, points P and Q are the feet of the perpendiculars from C to \overline{AB} and from B to \overline{AC}, respectively. Line PQ intersects the circumcircle of \triangle ABC in two distinct points, X and Y. Suppose XP=10, PQ=25, and QY=15. The value of AB\cdot AC can be written in the form m\sqrt n where m and n are positive integers, and n is not divisible by the square of any prime. 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.