Prove that circle A with center (–1, 1) and radius 1 is similar to circle B with center (–3, 2) and radius 2.

Answer 1

Translate circle A from center (-1,1) to (-3,2) by moving 2 units to the left and one unit up.

Then dilate by a scale factor of 2.

Since any two circles can be translated to have the same center, the dilation r2/r1 proves

the circles are similar where r1 and r2 are the radii of the circles.

Therefore, all circles are similar.

In this case r1=1 and r2=2, so the scale factor is r2/r1 = 2/1 = 2