The radius of a circle whose circumference is equal to the sum of the circumferences of the two circles of diameters 36 cm and 20 cm is

Diameter of first circle = d₁ = 36 cm

Diameter of second circle = d₂ = 20 cm

∴ Circumference of first circle = πd₁ = 36π cm

Circumference of second circle = πd₂ = 20π cm

Now, we are given that,

Circumference of circle = Circumference of first circle + Circumference of second circle

πD = πd₁ + πd₂

⇒ πD = 36π + 20π

⇒ πD = 56π

⇒ D = 56

⇒ Radius = 56/2 = 28 cm