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Let S be a square of unit area. Consider any quadrilateral which has one vertex on each side of S. If a,b, c and d denote the length of the side of the quadrilateral, prove that 2 ≤ a2 + b2 + c2 + d2 ≤ 4.

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Let the square S is to be bounded by the lines x = ±1/2 and y = ± 1/2

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