Question

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.

Answer 1

Radius (r₁) of 1^st circle = 19 cm

Radius (r₂) or 2^nd circle = 9 cm

Let the radius of 3^rd circle be r.

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

Circumference of 2^nd circle = 2πr₂ = 2π (9) = 18π

Circumference of 3^rd circle = 2πr

Given that,

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

2πr = 38π + 18π = 56π

`r = (56pi)/(2pi) = 28`

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