Let A,B,C,D and E be five points lying in this order on a circle, such that AD=BC. The lines AD and BC meet at a point F. The circumcircles of the triangles CEF and ABF meet again at the point P.Prove that the circumcircles of triangles BDF and BEP are tangent to each other. JBMOJBMO Shortlistgeometrycircumcircletangent circles