A circle is inscribed in an equilateral trian | vedclass

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(C) The radius $r$ of the incircle of an equilateral triangle with side $a = 6$ is given by $r = \frac{a}{2\sqrt{3}} = \frac{6}{2\sqrt{3}} = \sqrt{3}$

Vedclass · Accepted Answer

$6$

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(C) The radius $r$ of the incircle of an equilateral triangle with side $a = 6$ is given by $r = \frac{a}{2\sqrt{3}} = \frac{6}{2\sqrt{3}} = \sqrt{3}$.The square is inscribed in this circle,so the diagonal of the square is equal to the diameter of the circle.Diagonal of the square $d = 2r = 2\sqrt{3}$.Let the side of the square be $x$. Then $x\sqrt{2} = d = 2\sqrt{3}$.$x = \frac{2\sqrt{3}}{\sqrt{2}} = \sqrt{2} 	imes \sqrt{3} = \sqrt{6}$.Area of the square $= x^2 = (\sqrt{6})^2 = 6$.

$A$ circle is inscribed in an equilateral triangle of side length $6$. Find the area of the square inscribed in this circle.

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