IrMO 2017 Problem 3

Four circles are drawn with the sides of quadrilateral $ABCD$ as diameters. The two circles passing through $A$ meet again at $A'$ , two circles through $B$ at $B'$ , two circles at $C$ at $C'$ and the two circles at $D$ at $D'$ . Suppose the points $A',B',C'$ and $D'$ are distinct. Prove quadrilateral $A'B'C'D'$ is similar to $ABCD$ .