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)`

r = 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.

Answer 2

Given that,

Radius of 1^st circle (r₁) = 9 cm

Radius of 2^nd circle (r₂) = 19 cm

Let the radius of required circle be r cm.

According to the question,

Circumference of required circle = Sum of circumference of two circles

i.e., 2πr = 2π₁ + 2πr₂

⇒ 2πr = 2π(r₁ + r₂)

⇒ r = r₁ + r₂

⇒ r = 9 + 19

⇒ r = 28 cm.

Hence, radius of required circle is 28 cm.