Question 85
Let $ABC$ be an acute, non-isosceles triangle with $H$ is the orthocenter and $M$ is the midpoint of $AH$. Denote $O_1, O_2$ as the centers of circles pass through $H$ and respectively tangent to $BC$ at $B, C$. Let $X, Y$ be the ex-centers which respect to angle $H$ in triangles $HMO_1, HMO_2$. Prove that $XY$ is parallel to $O_1O_2$.