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.

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Solution

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.

Area of 1^st circle

Area of 2^nd circle

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.

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