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

Explanation

Let ABCD be a square having side` a` is inscribed in a circle of radius 'r'.

Now, the diameter of circle is the diagonal of square.

`:. BD = AC = 2r `

Applying pythagoras theorem in `/_\ ADC`

`AC^2 = AD^2 + CD^2`

`:. (2r)^2 = a^2 + a^2`

`:. 4r^2 = 2a^2`

` :. a^2 = 2r^2`

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