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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]  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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#GREpracticequestion In the figure below, ABC is a circular .jpg [ 17.98 KiB | Viewed 734 times ]

[Reveal] Spoiler: OA
24

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Re: In the figure below, ABC is a circular sector with center A. [#permalink]  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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