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Question
In a circle of radius 7 cm, a square ABCD is inscribed. Find the area of the circle which is outside the square.
Solution
Let the diagonal of the square be d.
We know that if a circle circumscribes a square, then the diameter of the circle is equal to the diagonal of the square.
∴ d = 2 × 7 = 14 cm
Now,
Area of required region = Area of circle - Area of square
`=pi"r"^2 - 1/2d^2`
`= 22/7 xx(7)^2 - 1/2xx(14)^2`
= 56 cm2
Hence, the required area is 56 cm2 .
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