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Question
A square is inscribed in a circle. Find the ratio of the areas of the circle and the square.
Solution
Let the side of the square be a and radius of the circle be r
We know that if a circle circumscribes a square, then the diameter of the circle is equal to the diagonal of the square.
`∴ sqrt(2a) = 2r`
`⇒ a = sqrt(2r)`
Now ,
`"Area of circle"/"Area of square" = (pi"r"^2)/"a"^2`
`= (pi"r"^2)/(sqrt(2r))^2`
`= ( pi"r"^2)/(2pi^2)`
`= pi/2`
Hence, the ratio of the areas of the circle and the square is π : 2
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