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A circle circumscribing an equilateral triangle with centroid at (0,0) of side \mathrm{'a'} is drawn and a square is drawn touching its four sides to circle. The equations of the circle circumscribing the square is

Option: 1

\mathrm{x^{2}+y^{2}=2 a^{2}}


Option: 2

\mathrm{3 x^{2}+3 y^{2}=2 a^{2}}


Option: 3

\mathrm{5 \mathrm{x}^{2}+5 \mathrm{y}^{2}=3 \mathrm{a}^{2}}


Option: 4

none of these


Answers (1)

best_answer

Centre (0,0)

\mathrm{AB}=\frac{\sqrt{3}}{2} \mathrm{a}
\mathrm{AO}=\frac{1}{\sqrt{3}} \mathrm{a}   \mathrm{\text{side of square }=\frac{2}{\sqrt{3}} \mathrm{a}}
\mathrm{\mathrm{OC}=\sqrt{\frac{2}{3}} \mathrm{a}}

\mathrm{\mathrm{x}^{2}+\mathrm{y}^{2}=\frac{2 \mathrm{a}^{2}}{3} \Rightarrow 3\left(\mathrm{x}^{2}+\mathrm{y}^{2}\right)=2 \mathrm{a}^{2}}

Posted by

Irshad Anwar

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