Given: The radius of circle Ois r, and the radius of circle X is r.

Prove: Circle Ois similar to circle X.

Step-by-step explanation:

Given:-

Circle "O" with radius 'r'

Circle "X" with radius 'r'

prove circle O is similar to X

It is to be remembered that any figures can be proven to be similar by similarity transformations which can map one circle onto another. These transformations range from rotation, reflection, dilation etc.

We would proceed in the following steps-

Independently map two circles O and X. Translate circle X on to circle O by vector XO. Now both the circles are concentric (since they have the same centre)

∴ Since the radius of both the circles are same hence the scaling factor is also 1.

∵Now since both circles have the same centre and same radius these circles are similar.