Question 56
Points $B$ and $C$ are fixed on the circle $\omega$. Denote by $M$ the midpoint of $BC$. Let $A$ be a variable point on $\omega$, and $H$ be the orthocenter of triangle $ABC$. The perpendicular from $H$ to $MH$ intersects lines $AB$ and $AC$ at points $X$ and $Y$, respectively. Prove that as point $A$ moves on $\omega$, the orthocenter of triangle $AXY$ also moves on a circle.