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