Question 111
In the isosceles triangle $ABC$, we have $AB = AC$ and $BC \gt AB$. $D$ and $M$ are the midpoints of $BC$ and $AB$ respectively. $X$ is a point that $BX \perp AC$ and $XD \parallel AB$. $H$ is the intersection of $BX$ and $AD$. If $P$ be the intersection of $DX$ with the circumcircle of $AHX$ (not $X$), prove that the tangent line in $A$ to the circumcircle of $AMP$ is parallel to $BC$.