KöMaL 2013 B4528

$k$ is the circumscribed circle of a cyclic quadrilateral ABCD . The centre of the inscribed circle of triangle ABC is $P$, and that of triangle ABD is $Q$. Let $E$ denote the midpoint of arc $BC$, and let $F$ denote the midpoint of arc $DA$ of the circle $k$. Prove that $PQ$ is parallel to $EF$.