A) \[2\sqrt{3}\]
B) \[\frac{3\sqrt{3}}{4}\]
C) \[\frac{2\sqrt{3}}{4}\]
D) None of these
Correct Answer: B
Solution :
Let r be the radius of the circle and x be the side of the square inscribed in it. Then, \[2{{x}^{2}}={{(2r)}^{2}}\,\Rightarrow \,2{{x}^{2}}=4{{r}^{2}}\] \[\Rightarrow \,\,{{x}^{2}}=2{{r}^{2}}=\] the area of the inscribed square Let ABCDEF be a hexagon inscribed in the same circle. Area of the hexagon \[=6\times \] Area of the equilateral triangle OBC \[=6\times \frac{\sqrt{3}}{4}\times {{r}^{2}}=\frac{3\sqrt{3}}{2}\,{{r}^{2}}\] Required ratio \[=\frac{\frac{3\sqrt{3}{{r}^{2}}}{2}}{2{{r}^{2}}}\,=\frac{3\sqrt{3}}{4}=3\sqrt{3}:4\]You need to login to perform this action.
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