KöMaL 2015 B4721

A circle $k$ touches the legs $AB$ and $AC$ of an isosceles triangle $ABC$ , and intersects the base $BC$ at $K$ and $L$ . Line segment $AK$ intersects the circle $k$ again at point $M$ . The reflections of point $K$ in $B$ and in $C$ are $P$ and $Q$ , respectively. Prove that $k$ is tangent to the circumscribed circle of triangle $PMQ$ .