A rectangle PQRS of maximum possible area is inscribed in a circle of centre O and radius a as shown. Find the shaded area outside the rectangle and inside the circle.
The rectangle has diagonal 2a, so side lengths x,y satisfy $x^2+y^2=4a^2$. Since $2xy\le x^2+y^2$, its maximum area is 2a², attained by a square. Subtract from the circle area πa² to obtain πa²−2a², C.
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