Two circles result

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?

Please install Java (version 1.4 or later) to use JavaSketchpad applets.

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?

This page uses JavaSketchpad, a World-Wide-Web component of The Geometer's Sketchpad. Copyright © 1990-2011 by KCP Technologies, Inc. Licensed only for non-commercial use.

Michael de Villiers, 6 August 2011.