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In the figure below, ABC is a circular sector with center A.
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14 Mar 2019, 10:45
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?
#GREpracticequestion In the figure below, ABC is a circular .jpg [ 17.98 KiB | Viewed 7128 times ]
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#GREpracticequestion In the figure below, ABC is a circular .jpg [ 17.98 KiB | Viewed 7128 times ]
Show: :: OA
24
Re: In the figure below, ABC is a circular sector with center A.
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20 Mar 2019, 16:51
20 Mar 2019, 16:51
1
Expert Reply
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.
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.
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Re: In the figure below, ABC is a circular sector with center A.
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01 Apr 2020, 08:00
01 Apr 2020, 08:00
1
Carcass wrote:
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?
Attachment:
#GREpracticequestion In the figure below, ABC is a circular .jpg
Show: :: OA
24
Here's the formula for finding the length of an arc:
GIVEN: arc BC has length \(4\pi\)
So, we can write: \((\frac{30}{360})(2\pi r) = 4\pi\)
Simplify the fraction: \((\frac{1}{12})(2\pi r) = 4\pi\)
Multiply both sides by \(12\) to get: \(2\pi r = 48\pi\)
Divide both sides by \(2\pi \) to get: \(r = 24\)
Since \(AC\) = the radius of the circle, we can see that \(AC = 24\)
Answer: 24
Cheers,
Brent
