Radius of first circle = r1 = 15 cm
Radius of second circle = r2 = 18 cm
∴ Circumference of first circle = 2πr1 = 30π cm
Circumference of second circle = 2πr2 = 36π cm
Let the radius of the circle = R
According to the question,
Circumference of circle = Circumference of first circle + Circumference of second circle
2πR= 2πr1+ 2πr2
⇒ 2πR = 30π + 36π
⇒ 66π ⇒ R = 33
⇒ Radius = 33 cm
Hence, required radius of a circle is 33 cm.