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# 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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