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