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Question
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.
Solution
Let the radius of the required circle be r.
Now, Area of the required circle = Area of circle having radius 8 cm + Area of circle having radius 6 cm
⇒ πr2 = π(8)2 + π(6)2
⇒ r2 = 64 + 36
⇒ r2 + 102
⇒ r = 10 cm
Hence, the radius of the circle is 10 cm.
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