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in Areas Related To Circles by (44.3k points)

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

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A square is inscribed in a circle (given)

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

So, length of the diagonal = 2r

Length of side of square = x = diagonal/√2 

= 2r/√2 

= √2r

Area of square = (side)2 = ( x)2 

= √2r × √2r 

= 2r2

Area of circle = πr2

Ratio of areas of circle and square = (area of the circle)/(area of square)

= πr2 / 2r2

= π/2

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

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