PL-OM 2012 Problem 3

Triangle $ABC$ with $AB = AC$ is inscribed in circle $o$ . Circles $o_1$ and $o_2$ are internally tangent to circle $o$ in points $P$ and $Q$ , respectively, and they are tangent to segments $AB$ and $AC$ , respectively, and they are disjoint with the interior of triangle $ABC$ . Let $m$ be a line tangent to circles $o_1$ and $o_2$ , such that points $P$ and $Q$ lie on the opposite side than point $A$ . Line $m$ cuts segments $AB$ and $AC$ in points $K$ and $L$ , respectively. Prove, that intersection point of lines $PK$ and $QL$ lies on bisector of angle $BAC$ .