We have given isosceles triangle $ABC$ with baseline $AB$. Point $M$ is midpoint of AB. Draw perpendicular line to side $AC$ through $M$ which intersects $AC$ in point $H$. Let $P$ be midpoint of $MH$. Show that lines $BH$ and $CP$ are perpendicular to each other.
I also have "hint": Construct height $BD$ to side $AC$ and look at the triangles $ABD$ and $MCH$.
Analytically there is no problem but I get stuck in geometrical approach to solution.