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* Given two circles of the same radius but with different centers, there is a translation of <math>\R^2</math> that sends one circle to the other. Namely, choose the translation that sends the center of the first circle, to the center of the second circle.

* The group of all orthogonal motions fixing the origin, sends each circle centered at the origin, to itself

[[File:Circle.png|800px]]

===Variant definitions===

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