# 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 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 = πr_{1}^{2}= π(8)^{2} = 64π sq. cm

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

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

πr^{2} = πr_{1}^{2 }+ πr_{2}^{2}

πr^{2} = 64π + 36π

πr^{2} = 100π

r^{2} = 100

r = ± 10

However, the radius cannot be negative.

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

**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:

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

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 is 10 cm