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In the figure below, ABC is a circular sector with center A.

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In the figure below, ABC is a circular sector with center A. [#permalink] New post 14 Mar 2019, 10:45
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In the figure below, ABC is a circular sector with center A. If arc BC has length \(4\pi\), what is the length of AC?

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[Reveal] Spoiler: OA
24

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Re: In the figure below, ABC is a circular sector with center A. [#permalink] New post 20 Mar 2019, 16:51
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The measure of the central angle is 30 degrees. This means it is equal to \(\frac{30}{360} = \frac{1}{12}\) of the entire circle.

This means that the area of ABC is 1/12 of the circle's area, and the length of arc BC is 1/12 of the circumference of the circle.

Since arc BC = \(4\pi\), the total circumference must be \(12(4\pi) = 48\pi\).

The circumference is equal to \(2\pi r\), where r is the radius. So:

\(2\pi r = 48\pi\)

Divide by \(2\pi\):

\(r = 24\)

Since AC is a radius, AC = 24.
Re: In the figure below, ABC is a circular sector with center A.   [#permalink] 20 Mar 2019, 16:51
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In the figure below, ABC is a circular sector with center A.

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