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Circling the Triangle

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January 2, 2009
geometryperimetercircumcircletrigonometryperpendicular bisectortrig identitiesLaw of Sines

Problem Statement

The number of inches in the perimeter of an equilateral triangle equals the number of square inches in the area of its circumscribed circle. What is the radius, in inches, of the circle? <spanclass=′latex−bold′>(A)</span> 32π<spanclass=′latex−bold′>(B)</span> 33π<spanclass=′latex−bold′>(C)</span> 3<spanclass=′latex−bold′>(D)</span> 6π<spanclass=′latex−bold′>(E)</span> 3π <span class='latex-bold'>(A)</span>\ \frac{3\sqrt2}{\pi} \qquad <span class='latex-bold'>(B)</span>\ \frac{3\sqrt3}{\pi} \qquad <span class='latex-bold'>(C)</span>\ \sqrt3 \qquad <span class='latex-bold'>(D)</span>\ \frac{6}{\pi} \qquad <span class='latex-bold'>(E)</span>\ \sqrt3\pi
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