Suppose that ABCD is a convex quadrilateral. Let F \equal{} AB\cap CD, E \equal{} AD\cap BC and T \equal{} AC\cap BD. Suppose that A,B,T,E lie on a circle which intersects with EF at P. Prove that if M is midpoint of AB, then \angle APM \equal{} \angle BPT. geometrycircumcircleratioprojective geometrygeometry proposed