In the figure below, CD and EF are the common internal tangents to the circles A and B. CF extended intersects the circles A and B at G and H, respectively. Prove that the chords CG and HF are congruent.

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This entry
contributed by Markus Heisss, Wurzburg, Bavaria. Published in:
"Die Wurzel - Zeitschrift fur Mathematik", Dec. 2005,
www.wurzel.org.
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Poster of problem 1380.