Question

what is the area of square that can be inscribed in a circle of radius r

Answer 1

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Answer 2

$\textsf{Join AC.Then ,AC is a diameter of the circle }$

$\rm \therefore AC=2r \: units$

$\rm But \: diagonal \: of \: a \: square=( \sqrt{2} ×side)$

$\rm \therefore \sqrt{2} \times \: side = 2r \implies \huge{\frac{2r}{ \sqrt{2} } }$

$\textsf{ \: Area of the square}= \rm ( { \sqrt{2} r})^{2} = 2r² \: sq. unit$