A square is inscribed in a circle. Find the ratio of the areas of the circle and the square.

Given:

A square is inscribed in a circle.

Let the radius of circle be ‘r’ and the side of the square be ‘x’.

⇒ The length of the diagonal = 2r

∵ Length of side of square =

∴ Length of side of square = = √2r

Area of square = side × side = x × x = √2r × √2r = 2r^{2}

Area of circle = πr^{2}

Ratio of areas of circle and square = = =

__Hence, the ratio of areas of circle and square is π:2.__

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