To prove that all circles are similar you would use the sequence of similarity

Two figures are similar are one of them can be obtained from the other with some transformations (reflections, translations, rotations, dilations) . The circle is defined by only one length - the radius.

To prove that all circles are similar you would use the sequence of similarity translation and dilation. A translation, followed by a dilation with scale factor r2/r1 will map one circle onto the other, thus proving that the circles are similar.

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