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.

Radius (r1) of 1st circle = 19 cm

Radius (r2) or 2nd circle = 9 cm

Now,

Let the radius of 3rd circle be r

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

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

Circumference of 3rd circle = 2πr

Given:

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

2πr = 38π + 18π = 56π

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