<p>If an arc of <img alt="$60^{\circ}$" height="13" src="https://latex.artofproblemsolving.com/0/8/d/08d5c45388de5c75af641c046d466de3592ffa98.png" width="24" /> on circle <img alt="$I$" height="14" src="https://latex.artofproblemsolving.com/0/2/7/027f4a11d6090f9eac0ce2488df6384dad1263ea.png" width="11" /> has the same length as an arc of <img alt="$45^{\circ}$" height="13" src="https://latex.artofproblemsolving.com/8/2/1/821d3f11ab7a3e93c7a404a34224228f0449505a.png" width="24" /> on circle <img alt="$II$" height="14" src="https://latex.artofproblemsolving.com/a/f/3/af3906651d16a548230a504127bc5b308a64068f.png" width="21" />, the ratio of the area of circle <img alt="$I$" height="14" src="https://latex.artofproblemsolving.com/0/2/7/027f4a11d6090f9eac0ce2488df6384dad1263ea.png" width="11" /> to that of circle <img alt="$II$" height="14" src="https://latex.artofproblemsolving.com/a/f/3/af3906651d16a548230a504127bc5b308a64068f.png" width="21" /> is:</p> <p><img alt="$\text{(A) } 16:9\quad \text{(B) } 9:16\quad \text{(C) } 4:3\quad \text{(D) } 3:4\quad \text{(E) } \text{none of these}$" height="17" src="https://latex.artofproblemsolving.com/2/b/f/2bf24f0b1b4b68dcac59d99299da20608fd6ad85.png" width="465" /></p>

Question No: 471

If an arc of $60^{\circ}$ on circle $I$ has the same length as an arc of $45^{\circ}$ on circle $II$ , the ratio of the area of circle $I$ to that of circle $II$ is:

$\text{(A) } 16:9\quad \text{(B) } 9:16\quad \text{(C) } 4:3\quad \text{(D) } 3:4\quad \text{(E) } \text{none of these}$

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Tags: Geometry

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