Let a be the side of a square sheet
Then area of bigger square sheet = a2 …..1
Now, we make the circle of maximum possible size from it.
Then the radius of circle = ………….2
So its diameter = a
Now, any square in a circle of maximum size will have the length of diagonal equal to the diameter of circle.
i.e. diagonal of square made inside the circle = a
so, the side of this square =
Area of this square =
From eqs.1and 2,
Area of final square is of original square.
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