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A circle C is drawn around a square S such that the sides of the squar

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A circle C is drawn around a square S such that the sides of the square become the four chords of the circle. What is the area of square S?

(1) Had a circle been drawn such that the four sides of square S were tangents to the circle, the area of the circle would be 30 square centimetres less than the area of circle C

(2) Had a circle been drawn with the diagonal of square S as its radius, the area of the circle have been 180 square centimetres more than the area of circle C

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