The diagonals of the cyclic quadrilateral ABCD intersect at the point E. Let P and Q are the centers of the circles circumscribed around the triangles BCE and DCE, respectively. A straight line passing through the point P parallel to AB, and a straight line passing through the point Q parallel to AD, intersect at the point R. Prove that the point R lies on segment AC. geometrycollinearcyclic quadrilateralUkraine Correspondence