Question

Prove that the two circles shown below are similar. (10 points) Circle B Has A Center Of (-1, 5) And A Radius Of 4. Circle D Has A Center Of (7, 4) And A Radius Of 2.
PLEASE HELP ASAP!

Answer 1

All circles are similar shapes.

However, we can prove that these circles are similar by finding their radius-circumference ratios.

Circle B

Radius:

• 4 units

Circumference:

• $C=2\pi r\\C=2\pi (4)\\C=8\pi$

Radius/circumference ratio:

• $\dfrac{4}{8\pi}\\\\\dfrac{1}{2\pi}$

Circle D

Radius:

• 2 units

Circumference:

• $C=2\pi r\\C=2\pi (2)\\C=4\pi$

Radius/circumference ratio:

$\dfrac{2}{4\pi}\\\\\dfrac{1}{2\pi}$

The radius/circumference ratio for both the circles is $\dfrac{1}{2\pi}$, thus making the two circles similar.