Circumcircle is tangent to the circumcircle

[Kazi_Zareer]

In $\triangle ABC$,$AB>AC$,let $H$ be $\triangle ABC$'s orthocenter,$M$ be $BC$'s midpoint.point $S$ is on $BC$ satisfies $\angle BHM=\angle CHS$.Point $P$ is on $HS$ so that $AP \perp HS$
Prove that the circumcircle of $\triangle MPS$ is tangent to the circumcircle of $\triangle ABC$

[asif e elahi]

Step 1: Let $\overrightarrow{MH}\cap \bigodot ABC=U$. Prove $U\in \bigodot ABC$.
Step 2: Let $\overrightarrow{AH}\cap \bigodot ABC=T$. Prove $T\in US$.

[Raiyan Jamil]

Invert circle $MPS$ and circle $ABC$ w.r.t. circle with diametre $BC$..... using miquel, radical axis the rest is easy....