Solution:

The first circle’s radius is 19 cm (given)

∴ 2π×19 = 38 cm is the circumference of the first circle.

The second circle’s radius is 9 cm (given)

The circumference of the second circle is 2π×9 , which is 18 cm.

So,

The circumference of two circles added together is 38π+18π = 56π cm.

Let R be the radius of the third circle.

The circumference of the third circle is equal to 2πR.

The circumference of two circles added together equals the circumference of the third circle.

As a result, 56π = 2πR

Alternatively, R = 28 cm.