In an acute-angled triangle $ABC, E$ and $F$ are the feet of the altitudes from $B$ and $C$, and $G$ and $H$ are the projections of $B$ and $C$ on $EF$, respectively. Prove that $HE = FG$.
Problem
Source: Switzerland - Swiss TST 2003 p2
Tags: equal segments, altitudes, perpendicular, geometry
