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.

Video Examples: Concentric Circles


Examples of Concentric Circles

      example of Concentric Circles
  • The above diagram shows two concentric circles having a common center O.

Solved Example onConcentric Circles

Ques: The circumferences of the two concentric circles are 72 ft and 48 ft. What is the difference between their radii? [Use p = 3.]
    example of Concentric Circles

Choices:

    A. 4 ft
    B. 5 ft
    C. 3 ft
    D. 6 ft
    Correct Answer: A

Solution:

    Step 1: Circumference of a circle = 2pr
    Step 2: Circumference of the outer circle is 72 ft. [Outer circle has greater circumference.]
    Step 3: 2pR = 72 [Radius of the outer circle is R.]
    ? 23 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: 2pr = 48 [Circumference of the inner circle is r.]
    ?23r = 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.