Geometry study guide

Question

Prove that the two circles shown below are similar.

https://cdn.flvs.net/assessment_images/educator_geometry_v19/09_08_9.gif

Answer 1

In Euclidean Geometry, all circles are similar because you can transform one circle into another by a translation and dilation. In your case, circle B is centered at (-1,5) and has a radius of 4. Circle D is centered at (7,4) with a radius of 2. You can transform circle B into circle D by:

1. Translating the center 8 units to the right and down one
2. Dilating the radius by a scale factor of 2/4 = 1/2 (Take the ratio of the radii of final circle to the starting circle)

Note that if the scale factor is 1, then the circles are congruent.