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Question
In figure, a square is inscribed in a circle of diameter d and another square is circumscribing the circle. Is the area of the outer square four times the area of the inner square? Give reasons for your answer.
Solution
Given diameter of circle is d.
∴ Diagonal of inner square = Diameter of circle = d
Let side of inner square EFGH be x.
∴ In right angled ΔEFG,
EG2 = EF2 + FG2 ...[By Pythagoras theorem]
⇒ d2 = x2 + x2
⇒ d2 = 2x2
⇒ x2 = `"d"^2/2`
∴ Area of inner square EFGH = (Side)2
= x2
= `"d"^2/2`
But side of the outer square ABCD = Diameter of circle = d
∴ Area of outer square = d2
Hence, area of outer square is not equal to four times the area of the inner square.
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