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.
Quick Summary
- Concentric circles share the same center.
- Concentric circles never have the same radius.
- The area between two concentric circles is called an annulus.
🍎 Teacher Insights
Use real-world examples like targets or ripples in a pond to illustrate the concept of concentric circles.🎓 Prerequisites
- Circles
- Radius
- Circumference
- Area
Check Your Knowledge
Q1: If the circumferences of two concentric circles are 72 ft and 48 ft, and π = 3, what is the difference between their radii?
Frequently Asked Questions
Q: What is the area between two concentric circles called?
A: The area between two concentric circles is called an annulus.
Q: Do concentric circles have the same radius?
A: No, concentric circles never have the same radius.