2019 AIME II Problem 15

In acute triangle A B C points P and Q are the feet of the perpendiculars from C to \overline{A B} and from B to \overline{A C}, respectively. Line P Q intersects the circumcircle of \triangle A B C in two distinct points, X and Y. Suppose X P=10, P Q=25, and Q Y=15. The value of A B \cdot A C 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.