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P01 [Geometry] - Turkish NMO 1st Round - 2004

Source:

November 12, 2013
geometrycircumcircleratioperimeter

Problem Statement

If the circumradius of a regular nn-gon is 11 and the ratio of its perimeter over its area is 433\dfrac{4\sqrt 3}{3}, what is nn?
<spanclass=′latex−bold′>(A)</span> 3<spanclass=′latex−bold′>(B)</span> 4<spanclass=′latex−bold′>(C)</span> 5<spanclass=′latex−bold′>(D)</span> 6<spanclass=′latex−bold′>(E)</span> 8 <span class='latex-bold'>(A)</span>\ 3 \qquad<span class='latex-bold'>(B)</span>\ 4 \qquad<span class='latex-bold'>(C)</span>\ 5 \qquad<span class='latex-bold'>(D)</span>\ 6 \qquad<span class='latex-bold'>(E)</span>\ 8
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