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jmc

geometry intermediate

Problem

If an arc of on circle has the same length as an arc of on circle , then what is the ratio of the area of circle to the area of circle ? Express your answer as a common fraction.
Solution
Let be the circumference of circle , let be the circumference of circle , and let the common length of the two arcs. Then Therefore Thus, the ratio of the areas is
Final answer
\frac{4}{9}