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# 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 (r₁) of the 1^{st} circle = 19 cm

Radius (r₂) of the 2^{nd} circle = 9 cm

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

Circumference of the 1^{st} circle = 2πr₁ = 2π (19) = 38π

Circumference of the 2^{nd} circle = 2πr₂ = 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 = 28

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.

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

**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

**Summary:**

If the radius of two circles are 19 cm and 9 cm respectively, the radius of the circle which has a circumference equal to the sum of the circumferences of the two circles is 28 cm.

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