Question 36
Assume that $ABCD$ is a cyclic quadrilateral with circumcircle $\Omega$. Assume lines $AB$ and $CD$ intersect at point $P$ and lines $AD$ and $BC$ intersect at $Q$. Let $\Gamma$ be the circumcircle of triangle $APQ$. Then $\Omega$ and $\Gamma$ intersect in two points, $A$ is one of them and $R$ is the other. Assume $C \neq R$. Prove that line $CR$ passes through $M$ where $M$ is the midpoint of linesegment $PQ$.