Problem

Source: 67 Polish MO 2016 Second Round - Problem 5

Tags: geometry, circle, Poland, quadrilateral, cyclic quadrilateral



Quadrilateral $ABCD$ is inscribed in circle. Points $P$ and $Q$ lie respectively on rays $AB^{\rightarrow}$ and $AD^{\rightarrow}$ such that $AP = CD$, $AQ = BC$. Show that middle point of line segment $PQ$ lies on the line $AC$.