**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}= 2r^{2}
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)

Perimeter of circle = 2 π (x/√2) = πx√2^{2}= πx^{2}/2
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