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
 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 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.
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