NTSE Stage 2 SAT 2017 Question Paper

Reason :
Let side of square be x units so, diameter of circle is also x units
$\Rightarrow \mathrm{OA}=\mathrm{OB}=\mathrm{OC}=$radius of circle $=\frac{2}{\mathit{x}}\mathrm{units}$
$\Rightarrow \mathrm{OD}=\frac{1}{2}$ [OA] by centroid properly that AO:OD
$=2:1$
⇒ $\mathrm{OD}=\frac{\mathrm{x}}{4}$ units
Now let side of this equilateral △ by y so by Pythagoras theorem
${\mathrm{AD}}^2+{\mathrm{DC}}^2={\mathrm{AC}}^2$
⇒ ${\left(\frac{3\mathrm{x}}{4}\right)}^2+{\left(\frac{\mathrm{y}}{2}\right)}^2={\mathrm{y}}^2$
⇒ ${\mathrm{x}}^2=\frac{4}{3}.\frac{4}{\sqrt{3}}\left(\frac{\sqrt{3}}{4}{\mathrm{y}}^2\right)$
That mean area of square $=\frac{16}{3\sqrt{3}}\times \mathrm{area}\mathrm{of}△$
Now area of square = K × area of △
means $\mathrm{K}=\frac{16}{3\sqrt{3}}$
Hence option (1) is correct