# The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles

**Solution:**

Using the formula of area of circle A = πr^{2}, we can find the radius of the circle.

The radius of the 1^{st} circle = 8 cm

The radius of the 2^{nd} circle = 6 cm

Let the radius of the 3 ^{rd} circle be equal to r.

Area of the 1^{st} circle = πr₁^{2}= π(8)^{2} = 64π sq.cm ------------ (1)

Area of the 2^{nd} circle = πr₂^{2} = π(6)^{2} = 36π sq.cm ----------- (2)

Given that, Area of the 3^{rd} circle = Area of the 1^{st} circle + Area of the 2^{nd} circle

πr^{2} = πr₁^{2 }+ πr₂^{2}

πr^{2} = 64π + 36π [From equation (1) and (2)]

πr^{2} = 100π

r^{2} = 100

r = ± 10

However, the radius cannot be negative. Thus, r = 10

Therefore, the radius of the circle having an area equal to the sum of the areas of the two circles is 10 cm.

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

**Video Solution:**

## The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles.

NCERT Solutions Class 10 Maths Chapter 12 Exercise 12.1 Question 2

**Summary:**

The radius of the circle having an area equal to the sum of the areas of the two circles of radii 8 cm and 6 cm respectively is 10 cm.

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