# 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.

**☛ Related Questions:**

- 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.
- Fig. 12.3 depicts an archery target marked with its five scoring regions from the centre outwards as Gold, Red, Blue, Black and White. The diameter of the region representing Gold score is 21 cm and each of the other bands is 10.5 cm wide. Find the area of each of the five scoring regions.
- The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 minutes when the car is travelling at a speed of 66 km per hour?
- Tick the correct answer in the following and justify your choice : If the perimeter and the area of a circle are numerically equal, then the radius of the circle is (A) 2 units (B) π units (C) 4 units (D) 7 units

visual curriculum