Question

Prove that the two circles shown below are similar. (10 points) Circle C is shown with a center at negative 3, 1 and a radius of 4. Circle E is shown with a center of 4, 9 and a radius of 3.

Answer 1

Answer:

Well, in reality, all circles are similar to each other. They will all have the same angles, and they don't really have side lengths. So, they are similar.

But to PROVE they are similar, we will transform Circle C to match circle E.

Circle C has a center at (-3, 1), and Circle E has a center of (4, 9). For Circle C to have the same center as Circle E, we will translate Circle C 7 units to the right, and 8 units up.

Since Circle C has a radius of 4, and Circle E has a radius of 3, dilate Circle C by a factor of 3/4. That way, the radius is 3 units as well.

And there you go! The two circles will map perfectly on top of each other.

Hope this helps!