Concentric Circles
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

Additional Links for Concentric Circles

• Click here for samples
• Back to Mathematics Dictionary