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A circle is inscribed in an equilateral triangle of side `adot`The area of any square inscribed in this circle is ______. |
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Answer» Correct Answer - `(a^(2))/(6)`sq unit In an equilateral triangle, the radius of incircle `=(1)/(3)xx` median of the triangle `=(1)/(3)sqrt(a^(2)-(a^(2))/(4))=(1)/(3)sqrt((4a^(2)-a^(2))/(4))=(a)/(2sqrt3)` therefore ,area of the square inscribed in this circle `=2("radius of circle")^(2) = (2a^(2))/(4*3)= (a^(2))/(6)` sq unit |
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