In circle BB, B, C, equals, 9BC=9 and the area of shaded sector = 9, pi9π. Find the length of arc, C, E, D CED⌢ . Express your answer as a fraction times piπ.
Question
In circle BB,
- B, C = 9
- 9BC = 9
- The area of shaded sector = 9π
Find the length of arc, . Express your answer as a fraction times .
Solution
The problem seems to be missing some information or the formatting is off, making it difficult to understand. However, I'll try to provide a general solution based on the information given.
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First, we need to find the radius of the circle. Since we know that the length of segment BC is 9, and B is the center of the circle, the radius of the circle is also 9.
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Next, we need to find the area of the entire circle. The formula for the area of a circle is πr², so the area of circle BB is π(9)² = 81π.
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We know that the area of the shaded sector is 9π. The fraction of the circle that the shaded sector represents is therefore 9π / 81π = 1/9.
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The circumference of the entire circle is 2πr = 2π(9) = 18π. The length of arc CED, which corresponds to the shaded sector, is therefore 1/9 of the total circumference, or (1/9) * 18π = 2π.
So, the length of arc CED is 2π.
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