Let ABC be a triangle with AB<AC and let M be the midpoint of AC. A point P (other than B) is chosen on the segment BC in such a way that AB=AP. Let D be the intersection of AC with the circumcircle of △ABP distinct from A, and E be the intersection of PM with the circumcircle of △ABP distinct from P. Let K be the intersection of lines AP and DE. Let F be a point on BC (other than P) such that KP=KF. Show that C, D, E and F lie on the same circle. cyclic quadrilateralgeometry