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Question

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


Solution

Let side of square be x cms inscribed in a circle.

Radius of circle (r)=12(diagonal of square)

=12(2x)=x2

Area of square = (side)2=x2

Area of circle =πr2=π(x2)2=πx22

Area of circleArea of square=πx22x2=π2=π:2

Ratio is π:2

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