By definition, a circle is the set of all the points in a plane that are equidistant from a fixed point called the center.
A dilation is a transformation that enlarges or reduces the size of a figure. Even though the new image has a different size, it will be similar to the original one. Let's perform a dilation on a circle.
As we can see, by performing a dilation on a circle we can obtain a circle of any radius we want. Therefore, given any two circles we can map one of them into the other by performing a dilation and/or a translation.
Since both translations and dilations are similarity transformations, we have that all circles are similar.
