If the sum of the circumferences of two circles with radii R₁ and R₂ is equal to the circumference of a circle of radius R, then
a. R₁ + R₂ = R
b. R₁ + R₂ > R
c. R₁ + R₂ < R
d. Nothing definite can be said about the relation among R₁, R₂ and R
Solution:
Given, radii of two circles are R₁ and R₂
The sum of the circumference of two circles is equal to the circumference of a circle of radius .
We have to find the relation between the radii of given circles.
We know that circumference of circle = 2πr
Circumference of circle with radius R₁ = 2πR₁
Circumference of circle with radius R₂ = 2πR₂
Circumference of circle with radius R = 2πR
Sum of the circumference of circle with radii R₁ and R₂ = 2πR₁ + 2πR₂
= 2π(R₁ + R₂)
Given, 2π(R₁ + R₂) = 2πR
Cancelling out common term,
R₁ + R₂ = R
Therefore, R₁ + R₂ = R
✦ Try This: If the sum of the circumferences of two circles with radii 3 cm and 4 cm is equal to the circumference of a circle of radius R, then radius R is equal to
Given, two circle with radii 3 cm and 4 cm
We have to find the radius R.
We know that circumference of circle = 2πr
Circumference of circle with radius 3 cm = 2π(3) = 6π
Circumference of circle with radius 4 cm = 2π(4) = 8π
Circumference of circle with radius R cm = 2πR
Sum of the circumferences of two circles with radii 3 cm and 4 cm = 6π + 8π = 14π
Given, 14π = 2πR
2R = 14
R = 7 cm
Therefore, the radius R is 7 cm
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 12
NCERT Exemplar Class 10 Maths Exercise 11.1 Problem 2
If the sum of the circumferences of two circles with radii R₁ and R₂ is equal to the circumference of a circle of radius R, then a. R₁ + R₂ = R, b. R₁ + R₂ > R, c. R₁ + R₂ < R, d. Nothing definite can be said about the relation among R₁, R₂ and R
Summary:
If the sum of the circumferences of two circles with radii R₁ and R₂ is equal to the circumference of a circle of radius R, then R₁ + R₂ = R
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