## 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*?

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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.