IR-TST 2010 Problem 6

Let $M$ be an arbitrary point on side $BC$ of triangle $ABC$ . $W$ is a circle which is tangent to $AB$ and $BM$ at $T$ and $K$ and is tangent to circumcircle of $AMC$ at $P$ . Prove that if $TK||AM$ , circumcircles of $APT$ and $KPC$ are tangent together.