Question 7
Let $ABC$ be a triangle, the circle having $BC$ as diameter cuts $AB$, $AC$ at $F$, $E$ respectively. Let $P$ be a point on this circle. Let $C_{0}$, $B_{0}$ be the projections of $P$ upon the sides $AB$, $AC$ respectively. Let $H$ be the orthocenter of the triangle $AB_{0}C_{0}$. Show that $\angle EHF = 90^{\circ}$.