Problem

Source: Saudi Arabia JBMO training test 2 2019, P4

Tags: geometry



Let ABCD be a cyclic quadrilateral in which AB = BC and AD =CD. Point M is on the small arc CD of the circle circumscribed to the quadrilateral. The lines BM and CD intersect at point P, and the lines AM and BD intersect at point Q. Prove that PQ is parralel to AC.