Question 161
Let $A$, $B$, $C$ be three points on a circle $\Gamma$ and consider points $M$, $N$ on the side $BC$, point $P$ on the side $AC$ and $Q$ on the side $BC$, such that $MP$ is parallel to $BC$ and $NQ$ is parallel to $AC$. Let $T$ be a point on line $MP$, so that $TC$ is tangent to $\Gamma$. The circumcircle of $\triangle TMN$ intersects $\Gamma$ at $K$ and $L$. Prove that $K$, $L$, $P$, $Q$ are collinear.