Question 3
Let $ABCD$ be a quadrilateral, such that $AB = BC = CD$. There are points $X, Y$ on rays $CA, BD$, respectively, such that $BX = CY$. Let $P, Q, R, S$ be the midpoints of segments $BX, CY, XD, YA$, respectively. Prove that points $P, Q, R, S$ lie on a circle.