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

Given:

Radius of one of the circles, C_{1} = 8 cm = r_{1}

Radius of the other circle, C_{2} = 6 cm = r_{2}

Let the other circle be C with radius ‘r’.

Area of C = Area of C_{1} + Area of C_{2} …… (i)

∵ Area of circle = πr^{2}

∴ Area of C_{1} = πr_{1}^{2} = × 8 × 8 =

and Area of C_{2} = πr_{2}^{2} = × 6 × 6 =

Using (i), we have

πr^{2} = + =

× r^{2} =

r^{2} = × = 100

r^{2} = 100

r = √100 = 10 or r = 10

__Hence, the radius of the circle is 10 cm.__

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