**Solution:**

Given,

The radius of the 1st circle = 8 cm

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

The radius of the 2nd circle = 6 cm

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

So,

The sum of the Area of two circles = 64𝜋 + 36𝜋 = 100𝜋

Now, assume that the radius of the 3rd circle = R

∴ The Area of the 3rd circle = 𝜋R^{2}

It is given that the area of the 3rd circle = Area of 1st circle + Area of 2nd circle

Or, 𝜋R^{2} = 100𝜋 cm^{2}

R^{2} ^{= }100 cm^{2
}So, R = 10 cm