Circle E has half the diameter of circle D. Circles D and E are internally tangential at C. Drag point A. What do you notice about the lengths of AB and BC?
Two circles result
Can you logically explain (prove) why your observation is true?
Can you generalize to when the smaller circle has diameter 1/k that of the larger circle?
Can you generalize to other shapes sharing a common point?
Michael de Villiers, 6 August 2011.