Question 108
Let $ABCD$ be a cyclic quadrangle and let $P$ be a point on the side $AB$. The diagonal $AC$ crosses the segment $DP$ at $Q$. The parallel through $P$ to $CD$ crosses the extension of the side $BC$ beyond $B$ at $K$, and the parallel through $Q$ to $BD$ crosses the extension of the side $BC$ beyond $B$ at $L$. Prove that the circumcircles of the triangles $BKP$ and $CLQ$ are tangent.