Question

If a square in inscribed in a circle, find the ratio of the areas of the circle and the square.

Answer 1

If AB = x, AC = x√2

Diameter of the circle = diagonal of the square
⇒ 2r = x√2

⇒ r = `(xsqrt2)/2`

Area of the circle = πr²
                            = π`((x sqrt2)/2)^2`

                            = π`(( x^2 2)/4)`

                            = `(πx^2)/2`

Area of the square = x²

Required ratio = `((πx^2)/2 )/x^2`

                        = `π/2`

                        = `22/7 xx 1/2`

                        = `11/7`
Hence, the required ratio is 11 : 7.