# Orthocenter

Author: mathforces
Problem has been solved: 12 times

Русский язык | English Language

Let $ABC$ be an acute-angled triangle in which $\omega$ is its circumscribed circle, and $H$ is the orthocenter. The tangent to the circumscribed circle of $\triangle HBC$ at the point $H$ intersects $\omega$ at the points $X$ and $Y$. It turned out that $HA = 3$, $HX = 2$, $HY = 6$. The area of $\triangle ABC$ can be written as $m \sqrt n$, where $m$ and $n$ are natural numbers and $n$ is not divisible by the square of any prime number. Find the value of $m + n$.