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Ratio of Areas Between Two Circles

Source: 1968 AHSME Problem #11

September 7, 2011
ratiogeometryAMC

Problem Statement

If an arc of 60∘60^\circ on circle I has the same length as an arc of 45∘45^\circ on circle II, the ratio of the area of circle I to that of circle II is:
<spanclass=′latex−bold′>(A)</span> 16:9<spanclass=′latex−bold′>(B)</span> 9:16<spanclass=′latex−bold′>(C)</span> 4:3<spanclass=′latex−bold′>(D)</span> 3:4<spanclass=′latex−bold′>(E)</span> None of these<span class='latex-bold'>(A)</span>\ 16:9 \qquad <span class='latex-bold'>(B)</span>\ 9:16 \qquad <span class='latex-bold'>(C)</span>\ 4:3 \qquad <span class='latex-bold'>(D)</span>\ 3:4 \qquad <span class='latex-bold'>(E)</span>\ \text{None of these}
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