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\begin{geothm}[Chou 1994 Example 1]
In triangle \( ABC \), let \( F \) the midpoint of the side \( BC \), \( D \) and \( E \) the feet of the altitudes on \( AB \) and \( AC \), respectively.  \( FG \) is perpendicular to \( DE \) at \( G \).  Show that \( G \) is the midpoint of \( DE \).
\end{geothm}
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