P124.3.0.2019.6.9 The point $M$ is the midpoint of the side $BC$ of triangle $ABC$. A circle is passing through $B$, is tangent to the line $AM$ at $M$, and intersects the segment $AB$ secondary at the point $P$.
Prove that the circle, passing through $A$, $P$, and the midpoint of the segment $AM$, is tangent to the line $AC$.