Question 44
Let $H$ and $O$ be the orthocenter and circumcenter of an acute triangle $ABC$ ($A$, $H$, $O$ are non-collinear). Suppose that $D$ is the projection of $A$ onto the line $BC$, and the perpendicular bisector of the segment $AO$ meets the line $BC$ at $E$. Prove that the midpoint of $OH$ is on the circumcircle of triangle $ADE$.
