Given a cyclic quadrilateral ABCD such that the tangents at points B and D to its circumcircle k intersect at the line AC. The points E and F lie on the circle k so that the lines AC,DE and BF parallel. Let M be the intersection of the lines BE and DF. If P,Q and R are the feet of the altitides of the triangle ABC, prove that the points P,Q,R and M lie on the same circle Concyclicaltitudescyclic quadrilateralgeometry