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