Question 2
(JAP 5) For an acute triangle $ABC$, $M$ is the midpoint of the segment $BC$, $P$ is a point on the segment $AM$ such that $PM=BM$, $H$ is the foot of the perpendicular line from $P$ to $BC$, $Q$ is the point of intersection of segment $AB$ and the line passing through $H$ that is perpendicular to $PB$, and finally, $R$ is the point of intersection of the segment $AC$ and the line passing through $H$ that is perpendicular to $PC$.
Show that the circumcircle of $\triangle QHR$ is tangent to the side $BC$ at point $H$.
Show that the circumcircle of $\triangle QHR$ is tangent to the side $BC$ at point $H$.