Question 15
Let $\triangle ABC$ be an acute triangle with circumcircle $\omega$ and orthocenter $H.$ 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 as $m\sqrt{n},$ where $m$ and $n$ are positive integers, and $n$ is not divisible by the square of any prime. Find $m + n.$