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Bunuel
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Ok this one is pretty easy...
Basically, if a square is inscribed in circle, the centre of square is the centre of circle.
Similarily, if a square is inscribed in a semi-circle(as in this case), the centre of the circle is the also the mid-point of the side of the square.

So,
AB= 2 x OB ------------------ (i)

Now take themeasure of a side of the square as "w",
Therfore, OB = \(\frac{w}{2}\) (as of step i)
OC= 20 (radius of the circle).

Now apply the pythagoras theorm,

\(w^2\) + \(\frac{ w^2}{4}\)= 400,

\(\frac{5w^2}{4}\) = 400 ,

Solving , we get \(w^2\) = 320 and hence the area of the square is 320 .

Do correct me if I am wrong. :)
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