Question 98
Let $ABCD$ be a cyclic quadrilateral inscribed in a circle $\Gamma$ such that $AB = AD$. Let $E$ be a point on the segment $CD$ such that $BC = DE$. The line $AE$ intersects $\Gamma$ again at $F$. The chords $AC$ and $BF$ meet at $M$. Let $P$ be the symmetric point of $C$ about $M$. Prove that $PE$ and $BF$ are parallel.