Question 123
The Euler circle of the acute-angled triangle $ABC$ is reflected with respect to the altitude from $A$ to $BC$, and it intersects the circumcircle of triangle $ABC$ at distinct points $X$ and $Y$ ($X \neq Y$). Let $H$ be the orthocenter of triangle $ABC$. Prove that $AH$ is the external angle bisector of $\angle XHY$.