The radii of two circles are 25 cm and 18 cm. Find the radius of the circle which has circumference equal to the sum of circumferences of these two circles.

Circumference of a circle = 2πr

For the first circle,

r₁ = 25 cm

Circumference₁ = 2 x π x 25 = 50π cm

For the second circle,

r₂ = 18 cm

Circumference₂ = 2 x π x 18 = 36π cm

Total circumference = Circumference₁ + Circumference₂

= 50π + 36π

= 86π cm

Let the radius of the new circle be R.

Circumference of the new circle = 2πR

86π = 2πR

86 = 2R

R = $\dfrac{86}{2}$

R = 43 cm

Hence, the radius of the new circle is 43 cm.