Problem

Source: Iran TST 2004

Tags: geometry, circumcircle, ratio, projective geometry, geometry proposed



Suppose that $ ABCD$ is a convex quadrilateral. Let $ F = AB\cap CD$, $ E = AD\cap BC$ and $ T = 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 = \angle BPT$.