Question

Prove that the two circles shown below are similar.

Answer 1

Answer:

We can prove the similarity of two circles by mapping one circle onto the other (i.e. making a circle look exactly like the other one) by a translation and a scale factor.

Let's map circle Y onto circle X for example. We need to make sure we have the same radii for both circles, so let's expand circle Y by a scale factor of 2. Then shift circle Y 6 units up and 6 units to the left to move the center point of circle Y over to that of circle X.

Now, since we could map circle Y onto circle X using transformations (scaling and translation), we know that the two circles are similar.