Question

given: circle a with a radius of 24 inches, and circle b with a radius of 8 inches
prove: circle a ~ circle b
use the drop - down arrows to select the correct answers to complete the proof.
two circles are similar if corresponding lengths are drop - down. the ratio of the radius of ⊙a to the radius of ⊙b is drop - down. the ratio of the circumference of ⊙a to the circumference of ⊙b is drop - down. therefore, ⊙a ~ ⊙b.

Explanation:

Step1: Recall similarity - ratio concept

Two circles are similar if corresponding lengths are proportional.

Step2: Calculate radius - ratio

The radius of circle A is $r_A = 24$ inches and of circle B is $r_B=8$ inches. The ratio of the radius of $\odot A$ to the radius of $\odot B$ is $\frac{r_A}{r_B}=\frac{24}{8} = 3$.

Step3: Calculate circumference - ratio

The circumference of a circle is $C = 2\pi r$. So $C_A=2\pi r_A$ and $C_B = 2\pi r_B$. Then $\frac{C_A}{C_B}=\frac{2\pi r_A}{2\pi r_B}=\frac{r_A}{r_B}=\frac{24}{8}=3$.

Answer:

1. Proportional
2. 3
3. 3