Try the following GRE quantitative reasoning question that tests your understanding of geometric relationship between circles and inscribed triangles.
Question#102:
If $p$ is the perimeter of an equilateral triangle inscribed in a circle, the area of the circle is:

$\quad \displaystyle \frac{\pi p^2}{3}$

$\quad \displaystyle \frac{\pi p^2}{9}$

$\quad \displaystyle \frac{\pi p^2}{27}$

$\quad \displaystyle \frac{\pi p^2}{81}$

$\quad \displaystyle \frac{\pi p^2 \sqrt{3}}{27}$
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