Question 91
In triangle $ABC$, $H$ is the orthocenter and $AK$ is an altitude. Circle $w$ goes through points $A$ and $K$ and intersects sides $AB$ and $AC$ at points $M$ and $N$ respectively. The line through point $A$ parallel to $BC$ intersects the circumscribed circles of triangles $AHM$ and $AHN$ a second time at points $X$ and $Y$ respectively. Prove that $XY = BC$.