The radii of two circles are 8 cm and 6 cm. Find the radius of the circle having area equal to the sum of the areas of the two circles.

Given:

Radius of one of the circles, C₁ = 8 cm = r₁

Radius of the other circle, C₂ = 6 cm = r₂

Let the other circle be C with radius ‘r’.

Area of C = Area of C₁ + Area of C₂ …… (i)

∵ Area of circle = πr²

∴ Area of C₁ = πr₁² = × 8 × 8 =

and Area of C₂ = πr₂² = × 6 × 6 =

Using (i), we have

πr² = + =

× r² =

r² = × = 100

r² = 100

r = √100 = 10 or r = 10

Hence, the radius of the circle is 10 cm.