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Which is greater: Length of arc ABC or 6?

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Which is greater: Length of arc ABC or 6? [#permalink] New post 29 Oct 2017, 01:31
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99% (00:17) correct 0% (00:00) wrong based on 7 sessions
Image

Quantity A
Quantity B
Length of arc ABC
6


A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given


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[Reveal] Spoiler:
Attachment:
Geometry - QC - circle arc length_q.PNG
Geometry - QC - circle arc length_q.PNG [ 6.69 KiB | Viewed 774 times ]
[Reveal] Spoiler: OA
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Re: Which is greater: Length of arc ABC or 6? [#permalink] New post 30 Oct 2017, 07:06
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The length of an arc is proportional to the correspondent angle at the center. Thus, given that the angle here is 60°, it is 1/6 of the entire angle of 360°. In the same way, the arc ABC is 1/6 of the full circumference that is \(2r\pi = 12\pi\). Then, the arc is \(\frac{1}{6}12\pi = 3\pi > 6\) long. Thus, quantity A is greater.

Answer A
Re: Which is greater: Length of arc ABC or 6?   [#permalink] 30 Oct 2017, 07:06
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Which is greater: Length of arc ABC or 6?

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