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 $PQ \parallel AB$.
Problem
Source: OLCOMA Costa Rica National Olympiad, Final Round, 2015 Shortlist G2 day2
Tags: parallel, geometry, congruent