Problem

Source: Sharygin Finals 2017, Problem 8.1

Tags: geometry, Projective



Let $ABCD$ be a cyclic quadrilateral with $AB=BC$ and $AD = CD$. A point $M$ lies on the minor arc $CD$ of its circumcircle. The lines $BM$ and $CD$ meet at point $P$, the lines $AM$ and $BD$ meet at point $Q$. Prove that $PQ \parallel AC$.