If two shapes of different sizes are similar, you can always transform one of them to make it map onto the other. For circles, the radius is the only thing that decides its size. We see two examples below.
If we shrink the left circle's radius by a factor of dilation of 12, it will also have a radius of 1, making it the same size as the right circle.
In fact, no matter what radius a circle has, we can always dilate it so that it has the same radius as any another circle. Assuming that the midpoints of two circles with different size do not coincide, we have to perform both a dilation and a translation to make them carry onto each other.
b
Any shape with the same number of vertices and with all sides of equal lengths — regular polygons — will be similar to each other. This is because no matter what sides you choose, the ratio of their sides will always be the same.
Therefore, any regular polygon with an arbitrary number of vertices will always be similar to another regular polygon with the same number of vertices.
Extra
Similarity and angles
Another way to look at it is that all angles in a regular polygon are congruent. This means their measures do not depend on the length of the sides, but on the number of vertices. Therefore, two regular polygons with the same number of vertices will have congruent angles, making them similar shapes.
