# The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles

**Solution:**

Using the formula of the circumference of circle C = 2πr, we find the radius of the circle.

Radius (r) of the 1^{st} circle = 19 cm

Radius (r) of the 2^{nd} circle = 9 cm

Let the radius of the 3^{rd} circle is r.

Circumference of the 1^{st} circle = 2πr_{1} = 2π (19) = 38π

Circumference of the 2^{nd} circle = 2πr_{2} = 2π (9) = 18π

Circumference of the 3^{rd} circle = 2πr Given that,

Circumference of the 3^{rd} circle = Circumference of the 1^{st} circle + Circumference of the 2^{nd} circle

2πr = 38π + 18π

2πr = 56π

r = 56π/2π

r = 28π

Therefore, the radius of the circle that has a circumference equal to the sum of the circumference of the two given circles is 28 cm.

**Video Solution:**

## The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles

### NCERT Solutions Class 10 Maths - Chapter 12 Exercise 12.1 Question 1:

The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles

The radius of the circle which has a circumference equal to the sum of the circumference of the given two circles of radii 19 cm and 9 cm is 28 cm