Composing Two Dilations

In the sketch below, ΔABC and ΔA'B'C' are related by a dilation with scale factor d1. ΔA'B'C' and ΔA"B"C" are related by a dilation with scale factor d2. Find the center of each of these two dilations.

ΔABC and ΔA"B"C" are also related by a dilation. Find the center of this dilation, and find the scale factor.

Look at the three dilation centers! How are they related?
Look at the three scale factors! How are they related?
Try to PROVE these astounding results!

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Steve Phelps, Created with GeoGebra