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