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Question 3
In Fig, 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.

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Solution

Given diameter of circle is d

Diagonal of inner square = Diameter of circle = d

Let side of inner square EFGH be x

EG2=EF2+FG2 [ by Pythagoras theorem]

d2=x2+x2

d2=2x2x2=d22

Area of inner square EFGH =(side)2=x2=d22

But side of the outer square ABCD = Diameter of circle = d

Area of outer square =d2

Hence, area of outer squares is not equal to four times the area of the inner square.

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