Perimeter of the circle \(= 2 * \pi\sqrt{x}\)

So, radius of circle \(= \sqrt{x}\)

Diameter of the circle = Diagonal of the square \(= 2\sqrt{x}\)

Area of circle \(= \pi (\sqrt{x})^2 = \pi x\)

Area of square \(= \frac{(2\sqrt{x})^2}{2} = 2x\)

Area of the yellow shaded region \(= \pi x - 2x\)

Attachment:

rhom.png [ 11.37 KiB | Viewed 7254 times ]
Probability of NOT falling in inscribed square = Probability of FALLING in the shaded regionProbability \(= \frac{\pi x - 2x}{\pi x} = 1 - \frac{2}{\pi}\)

Bunuel: Kindly update the OA

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