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# If the sum of the areas of two circles with radii R₁ and R₂ is equal to the area of a circle of radius R, then

a. R₁ + R₂ = R

b. R₁² + R₂² = R²

c. R₁ + R₂ < R

d. R₁^{2 }+ R₂^{2 }< R²

**Solution:**

Given, radii of two circles are R₁ and R₂

Sum of the areas of two circles is equal to the __circumference of the circle__ with radius R.

We have to find the relation between the radii of the given circles.

Area of the circle = πr²

Now, __area of circle__ with radius R₁ = πR₁²

Area of circle with radius R₂ = πR₂²

Sum of the areas = πR₁² + πR₂²

= π(R₁² + R₂²)

Area of circle with radius R = πR²

Given, π(R₁² + R₂²) = πR²

Cancelling out common term,

(R₁² + R₂²) = R²

Therefore, R₁² + R₂² = R²

**✦ Try This:** If the sum of the areas of two circles with radii 5 cm and 8 cm is equal to the area of a circle of radius R, then radius R is equal to

Given, area of two circles are 5 cm and 8 cm

We have to find the radius R.

Area of circle = πr²

Area of circle with radius 5 cm = π(5)²

= 25π

Area of circle with radius 8 cm = π(8)²

= 64π

Area of circle with radius R cm = πR²

Sum of areas of circle with radius 5 cm and 8 cm = 25π + 64π

= 89π

Given, 89π = πR²

R² = 89

Taking __square root__,

R = √89

R = 9.43 cm

Therefore, the radius R is 9.43 cm

**☛ Also Check: **NCERT Solutions for Class 10 Maths Chapter 12

**NCERT Exemplar Class 10 Maths Exercise 11.1 Problem 1**

## If the sum of the areas of two circles with radii R₁ and R₂ is equal to the area of a circle of radius R, then a. R₁ + R₂ = R, b. R₁² + R₂² = R², c. R₁ + R₂ < R, d. R₁² + R₂² < R²

**Summary:**

If the sum of the areas of two circles with radii R₁ and R₂ is equal to the area of a circle of radius R, then R₁² + R₂² = R²

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