BMO Round 1, 2015

Geometry Difficulty 7.0 National Olympiad, round 2 Prove it United Kingdom

Let $ABCD$ be a cyclic quadrilateral. Let $F$ be the midpoint of the arc $AB$ of its circumcircle which does not contain $C$ or $D$ . Let the lines $DF$ and $AC$ meet at $P$ and the lines $CF$ and $BD$ meet at $Q$ . Prove that the lines $PQ$ and $AB$ are parallel.

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