IR-TST 2010 Problem 8

Let $ABC$ an isosceles triangle and $BC>AB=AC$ . $D,M$ are respectively midpoints of $BC, AB$ . $X$ is a point such that $BX\perp AC$ and $XD||AB$ . $BX$ and $AD$ meet at $H$ . If $P$ is intersection point of $DX$ and circumcircle of $AHX$ (other than $X$ ), prove that tangent from $A$ to circumcircle of triangle $AMP$ is parallel to $BC$ .