Question 38
Given a cyclic quadrilateral $ABCD$ with circumcenter $O$. Let $E$ be the intersection of $AD$ and $BC$, and $F$ be the intersection of $AC$ and $BD$. Circle $\omega$ is tangent to $BD$ and $AC$. $QP$ is a diameter of $\omega$ such that $F$ is the orthocenter of triangle $QEP$. Prove that $EO$ passes through the center of $\omega$.