Question 75
A circle passing through vertices $B$ and $C$ of triangle $ABC$ intersects sides $AC$ and $AB$ at points $D$ and $E$, respectively. If $P$ is the intersection point of $BD$ and $CE$, $H$ is the foot of the perpendicular line from $P$ to $AC$ and $M$ and $N$ are the midpoints of $BC$ and $AP$, prove that triangles $MNH$ and $CAE$ are similar.