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