The circumference of a circle is equal to the sum of the circumferences of two circles having diameters 36 cm and 20 cm. The radius of the new circle is
A. 16 cm

B. 28 cm

C. 42 cm

D. 56 cm

Let the bigger circle be C₁ and other circles be C₂ and C₃

Radius of circle C₁ = r₁

Diameter of circle C₂ = 36 cm

Radius of circle C₂ = r₂ = 36/2 cm = 18cm

Diameter of circle C₃ = 20 cm

Radius of circle C₃ = r₃ = 20/2 cm = 10 cm

Circumference of circle C₂ = 2πr₂

= 2 × π × 18 cm = 36π cm

Circumference of circle C₃ = 2πr₃

= 2 × π × 10 cm = 20π cm

Circumference of circle C₁ = Circumference of circle C₂ + Circumference of circle C₃

⇒ 2πr₁ = 2πr₂ + 2πr₃

⇒ 2πr₁ = 36π + 20π

⇒ 2πr₁ = 56π

⇒ r₁ = 28 cm

Radius of circle C₁ = r₁ = 28 cm