When a square is inscribed in a circle, then
Diagonal of
the Square = Diameter of the Circle
(1) If the radius of the circle is given as ‘r’, then area/perimeter of the square can be determined as given below:
Diagonal of square = Diameter of circle = 2r
=> side of square = (2r)/√2 = r√2
=> side of square = (2r)/√2 = r√2
=> Area of square = (r√2)2 = 2r2
Perimeter of square = 4(r√2) = 4√2r
(2) If the side of the square is given as ‘x’, then area/perimeter of the circle can be determined as given below:
Diameter of circle = Diagonal of square = x√2
=> Radius of circle = x√2/2 = x/√2
=> Radius of circle = x√2/2 = x/√2
=> Area of circle = π(x/√2)2 = πx2/2
Perimeter of circle = 2 π (x/√2) = πx√2
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