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If a square is inscribed in a circle of radius r as shown below, then the area of the square region is______

If a square is inscribed in a circle of radius r as shown below, then the area of the square region is______ Correct Answer 2r2

Since the radius is r, the circle’s diameter = diagonal of square = 2r.Since diagonal = side√2:2r = side√22r/√2 = sideThus, area of the square = (2r/√2)^2 = 4r^2/2= 2r^2.

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