AT-OEMO-BEG 2013 Problem 4

Let $ABC$ be an acute-angled triangle and $D$ a point on the altitude through $C$ . Let $E$ , $F$ , $G$ and $H$ be the midpoints of the segments $AD$ , $BD$ , $BC$ and $AC$ . Show that $E$ , $F$ , $G$ , and $H$ form a rectangle.

(G. Anegg, Innsbruck)