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Equilateral triangle inscribed in a circle

Source: 1959 AHSME Problem 21

August 13, 2013
geometryperimeterratioLaTeXAMCcircleAMC 12

Problem Statement

If pp is the perimeter of an equilateral triangle inscribed in a circle, the area of the circle is: <spanclass=′latex−bold′>(A)</span> πp23<spanclass=′latex−bold′>(B)</span> πp29<spanclass=′latex−bold′>(C)</span> πp227<spanclass=′latex−bold′>(D)</span> πp281<spanclass=′latex−bold′>(E)</span> πp2327 <span class='latex-bold'>(A)</span>\ \frac{\pi p^2}{3} \qquad<span class='latex-bold'>(B)</span>\ \frac{\pi p^2}{9}\qquad<span class='latex-bold'>(C)</span>\ \frac{\pi p^2}{27}\qquad<span class='latex-bold'>(D)</span>\ \frac{\pi p^2}{81} \qquad<span class='latex-bold'>(E)</span>\ \frac{\pi p^2 \sqrt3}{27}
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