Question 11
Let $ABC$ be a triangle and $H_C$ the foot of the altitude from $C$. Let $P$ be a point on the segment $[CH_C]$ (other than $C$), and let $E, F, G, H$ be the midpoints of $[AP]$, $[BP]$, $[BC]$, $[AC]$, respectively. Show that $EFGH$ is a rectangle.