Radius (r1) of 1^{st} circle = 8 cm

Radius (r2) of 2^{nd} circle = 6 cm

Let the radius of 3^{rd} circle be r.

Given that,

Area of 3^{rd} circle = Area of 1^{st} circle + Area of 2^{nd }circle

However, the radius cannot be negative. Therefore, the radius of the circle having area equal to the sum of the areas of the two circles is 10 cm.