SHARYGIN 2021 Problem 19

A point $P$ lies inside a convex quadrilateral $ABCD$ . Common internal tangents to the incircles of triangles $PAB$ and $PCD$ meet at point $Q$ , and common internal tangents to the incircles of $PBC,PAD$ meet at point $R$ . Prove that $P,Q,R$ are collinear.