2020 AIME I Problem 15

Let \triangle ABC be an acute triangle with circumcircle \omega, and let H be the intersection of the altitudes of \triangle ABC. Suppose the tangent to the circumcircle of \triangle HBC at H intersects \omega at points X and Y with HA=3,HX=2, and HY=6. The area of \triangle ABC 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.