Question 96
Let $O$ be the circumcenter and $H$ the orthocenter of triangle $ABC$, and suppose that $OH$ is parallel to $BC$. Let $AH$ meet the circumcircle of triangle $ABC$ again at $X$ ($X \neq A$), and let $XB, XC$ meet $OH$ at $Y, Z$, respectively. Let $P$ be the projection of $Y$ onto $AB$ and $Q$ the projection of $Z$ onto $AC$. Prove that $PQ$ bisects segment $BC$.