A quadrilateral ABCD is inscribed in a circle. The lines AB and CD intersect at point E, and the lines AD and BC intersect at point F. The bisector of the angle AEC intersects the side BC at the point M and the side AD at the point N; and the bisector of the angle BFD intersects the side AB at the point P and the side CD at the point Q. Prove that the quadrilateral MPNQ is a rhombus.
rhombusgeometrycyclic quadrilateral