Radius (r1) of 1st circle = 8 cm

Radius (r2) of 2nd circle = 6 cm

Let the radius of 3rd circle be r

Area of 1^stcircle = r1² = π (8)² = 64π

Area of 2^nd circle = πr2² = π (6)² = 36 π

Given that,

Area of 3rd circle = Area of 1st circle + Area of 2nd circle

πr² = πr1² + πr2²

πr² = 64 π + 36 π

πr² = 100 π

r² = 100

r =

But we know that the radius cannot be negative. Hence, the radius of the circle having area equal to the sum of the areas of the two circles is 10 cm