The radii of two circles are 20 cm and 13 cm, respectively. Find the radius of the circles which has a circumference equal to the sum of the circumference of the two circles.

33 cm

We know that,

Circumference of the circle = 2πr 

We have,

The radii of two circles = 20 cm and 13 cm

Let the radius of the bigger circle = R cm 

then, Circumference of bigger circle = 2π R = 2π × 20 = 40π 

Circumference of circle (radius = 13 cm) = 2π × 13 = 26π 

According to the question  = 2π R = 40π + 26π 

= 2π R = 66 π 

R = 33 cm