CR-MO 2015 G5

Let $A, B, C, D$ be points that lie on the same circle . Let $F$ be such that the arc $AF$ is congruent with the arc $BF$ . Let $P$ be the intersection point of the segments $DF$ and $AC$ . Let $Q$ be intersection point of the $CF$ and $BD$ segments. Prove that $PQ \parallel AB$ .