Question 17
Let $\Gamma$ be the circumcircle and $O$ be the circumcenter of a triangle $ABC$ with $AC \neq BC$. The tangent line to $\Gamma$ drawn by $C$ intersects the line $AB$ at $M$. The line perpendicular to $OM$ drawn by $M$ cuts the lines $BC$ and $AC$ at $P$ and $Q$, respectively. Show that the segments $PM$ and $MQ$ are equal.