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

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

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Given,

Radii of the two circles are 6 cm and 8 cm

Area of circle with radius 8 cm = π (8)2 = 64π cm2

Area of circle with radius 6cm = π (6)2 = 36π cm2

Sum of areas = 64π + 36π = 100π cm2

Let the radius of the circle be x cm

Area of the circle = 100π cm2 (from above)

πx= 100π

x = √100 = 10 cm

Therefore, the radius of the circle is 10 cm.