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

Radius (*r*1) of 1st circle = 8 cm

Radius (*r*2) of 2nd circle = 6 cm

Let the radius of 3rd circle be *r*

Area of 1^{st}circle = r1^{2} = π (8)^{2} = 64π

Area of 2^{nd} circle = πr2^{2} = π (6)^{2} = 36 π

Given that,

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

πr^{2} = πr1^{2} + πr2^{2}

πr^{2} = 64 π + 36 π

πr^{2} = 100 π

r^{2} = 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

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