IR-TST 2004 Problem 3

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 $\angle APM = \angle BPT$ .