PL-OM 2012 Problem 5

Point $O$ is a center of circumcircle of acute triangle $ABC$ , bisector of angle $BAC$ cuts side $BC$ in point $D$ . Let $M$ be a point such that, $MC \perp BC$ and $MA \perp AD$ . Lines $BM$ and $OA$ intersect in point $P$ . Show that circle of center in point $P$ passing through a point $A$ is tangent to line $BC$ .