** Definition of Concentric Circles**

- Two or more circles are said to be concentric if they have the same center.

**More about Concentric Circles**

- Two concentric circles never have the same radius.
- The area between two concentric circles is called annulus.

**Example of Concentric Circles**

- The above diagram shows two concentric circles having a common center O.

**Solved Example on Concentric Circles**

The circumferences of the two concentric circles are 72 ft and 48 ft. What is the difference between their radii? [Use π = 3.]

Choices:

A. 4 ft

B. 5 ft

C. 3 ft

D. 6 ft

Correct Answer: A

Solution:

Step 1:Circumference of a circle = 2πr

Step 2:Circumference of the outer circle is 72 ft. [Outer circle has greater circumference.]

Step 3:2πR = 72 [Radius of the outer circle is R.]

⇒2×3 ×R = 72

Step 4:R = 12 ft [Simplify.]

Step 5:Circumference of the inner circle is 48 ft. [Inner circle has lesser circumference.]

Step 6:2πr = 48 [Circumference of the inner circle is r.]

⇒2×3×r = 48

Step 7:r = 8 ft [Simplify.]

Step 8:The difference between the radii = R - r

Step 9:= 4 [Substitute R = 12 and r = 8 and Subtract.]

Step 10:The difference between the two radii = 4 ft.

**Related Terms for Concentric Circles**

- Center
- Radius