Question

the radius of the circle and 19 cm and 9 cm find the radius of a circle which has a circumference equal to the sum of the two circumference

Answer 1

let the radius of the required cicle ber cm
so 2×22/7 ×r =2×22/7(19+9)
or r=28 (ans)

Answer 2

Hi !

Radius of bigger circle = 19 cm = R
Radius of smaller circle = 9 cm = r 

Circumference of bigger circle + Circumference of smaller circle = circumference of new circle 

Let the radius of the new circle be R'

so ,

2πR + 2πr  = 2πR'
2π × (R + r) = 2π × R'

2π gets cancelled on both sides,

R + r = R'

19 + 9 = R'

28 = R'

Hence,

Radius of new circle = R' = 28 cm

Hope this helps you !