Question 98
Let $ABC$ be a scalene triangle with circumcenter $O$ and orthocenter $H$. A point $P$ inside triangle $AHO$ satisfies $\angle AHP=\angle POA$. Let $M$ be the midpoint of $OP$. Lines $BM,CM$ meet the circumcircle of $ABC$ again at $X,Y$, respectively. Prove that $XY$ passes through the circumcenter of triangle $APO$.