Question

area of squre inscribed in a circle of radius r is

Answer 1

Hey!!!!

Good Evening

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We have a circle with radius r

Then d = 2r

Here the diameter of the circle becomes the diagonal of the square

Thus area of the square
$= > \frac{1}{2} {diagonal}^{2}$

Thus

=> 1/2 x 4r²

=> 2r² (Answer)

Thus the area of the incribed square is 2r²

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Hope this helps ✌️

Note : This formula of area of square is rarely used

Answer 2

Your answer

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

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

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

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

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