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Arc Ratio

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February 11, 2008
ratiogeometry

Problem Statement

If an arc of 45∘ 45^\circ on circle A A has the same length as an arc of 30∘ 30^\circ on circle B B, then the ratio of the area of circle A A to the area of circle B B is <spanclass=′latex−bold′>(A)</span> 49<spanclass=′latex−bold′>(B)</span> 23<spanclass=′latex−bold′>(C)</span> 56<spanclass=′latex−bold′>(D)</span> 32<spanclass=′latex−bold′>(E)</span> 94 <span class='latex-bold'>(A)</span>\ \frac {4}{9} \qquad <span class='latex-bold'>(B)</span>\ \frac {2}{3} \qquad <span class='latex-bold'>(C)</span>\ \frac {5}{6} \qquad <span class='latex-bold'>(D)</span>\ \frac {3}{2} \qquad <span class='latex-bold'>(E)</span>\ \frac {9}{4}
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