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’.


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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 = 2r2


Area of circle = πr2


Ratio of areas of circle and square = = =


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


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