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
Edit Lesson