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A circle is inscribed in an equilateral ...

A circle is inscribed in an equilateral triangle of side length a. The area of any square inscribed in the circle is

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`tan30=r/(a/2)`
`r=(a/(2sqrt3))`
Side of square=`2(rsin45)`
`=2*(a/(2sqrt3*sqrt2))`
`a'=a/sqrt6`
Area of square=`a^2/6`.
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