Rule

Similar Circles Theorem

All circles are similar.

In the diagram, ⊙ B ~ ⊙ A.

Proof

Two figures are similar if there is a composition of transformations that maps one figure onto the other. In this case, ⊙ A can be mapped onto ⊙ B by a composition of a translation and a dilation.

transformations

Therefore, these two circles are similar. By following the same procedure, any two circles can be proven to be similar.

Exercises
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