Question

Two circles are concentric. A central angle forms an arc on both circles. The length of the arc on the smaller circle is 21 inches and the length of the arc on the larger circle is 51 inches. If the larger circle has a radius of 11 inches, what is the radius of the smaller circle?

A. 8.3 inches
B. 16.9 inches
C. 4.5 inches
D. 20.4 inches

Answer 1

[AI-generated answer — Bot GPT 3.5]

C. 4.5 inches

To find the radius of the smaller circle, we can set up a proportion:

(Length of arc on larger circle) / (Radius of larger circle) = (Length of arc on smaller circle) / (Radius of smaller circle)

Plugging in the values:
51 / 11 = 21 / x

Solving for x:
x = (11 * 21) / 51
x = 4.5

Therefore, the radius of the smaller circle is 4.5 inches.