Question 94
Given triangle $ABC$ and its circumcircle. Point $P$ is midpoint of arc $BAC$. Circle with diameter $CP$ cuts angle bisector of $\angle BAC$ at points $K, L$ (point $K$ lies closer to $A$ than $L$). Point $M$ is symmetric to $L$ with respect to line $BC$. Prove that circumcircle of triangle $BKM$ bisects segment $BC$.