﻿ Definition of Concentric Circles | Define Concentric Circles - Geometry - Free Math Dictionary Online

# Concentric Circles

## Definition of Concentric Circles

Two or more circles are said to be concentric if they have the same center.

• Two concentric circles never have the same radius.
• The area between two concentric circles is called annulus.

### Examples of Concentric Circles

• The above diagram shows two concentric circles having a common center O.

A. 4 ft
B. 5 ft
C. 3 ft
D. 6 ft

### 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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