Question

Explain how to use the figure below and a sequence of similarity transformations to prove that all circles are similar.

Answer 1

Translate circle A (blue), so that its center is the same with circle B (black)

A dilation is needed to increase the size of circle A to coincide with circle B. Let x be the value when multiply by r will create s.

The scale factor , x, to increase circle A is

`\begin{gathered} x\cdot r=s\longrightarrow x=(s)/(r) \\ \\ \text{A translation, followed by a dilation with scale factor }(s)/(r)\text{ will map one circle} \\ \text{onto the other, thus proving that all circles are similar.} \end{gathered}`