Question 81
Let $ABCD$ be a square inscribed in circle $(O)$. Let $P$ be a point on the minor arc $CD$ of $(O)$. Line $PB$ intersects $AC$ at $E$. Line $PA$ intersects $DB$ at $F$. The circumcircle of triangle $PEF$ cuts $(O)$ again at $Q$. Prove that $PQ$ is parallel to $CD$.