Similar Circles

 

You may be surprised to learn that two noncongruent circles that lie in the same plane and have no common interior points can be mapped one onto the other by more than one dilation.

 

 

1. Here is diagram that suggests one way to map a smaller circle onto a larger one using a dilation. The circles are given. The lines suggest how to find the center for the dilation. Describe how the center is found. Use segments in the diagram to name the scale factor.

 

2. Here is another pair of noncongruent circles with no common interior point. From exercise 1, you know you can locate a point off to the left of the smaller circle that is the center for a dilation mapping circle C onto circle C`. Find another center for another dilation that maps circle C onto circle C`. Mark and label segments to name the scale factor.