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If the diameter of the circle is 36, what is the length of a

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GMAT Club Legend
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If the diameter of the circle is 36, what is the length of a [#permalink] New post 19 Sep 2018, 17:55
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Question Stats:

35% (02:26) correct 64% (00:50) wrong based on 14 sessions
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If the diameter of the circle is 36, what is the length of arc ABC?

(A) \(8\)
(B) \(8\pi\)
(C) \(28\pi\)
(D) \(32\pi\)
(E) \(56\pi\)
[Reveal] Spoiler: OA

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Re: If the diameter of the circle is 36, what is the length of a [#permalink] New post 20 Sep 2018, 21:56
explain how c can be the answer??
GMAT Club Legend
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Joined: 07 Jun 2014
Posts: 4749
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Re: If the diameter of the circle is 36, what is the length of a [#permalink] New post 24 Sep 2018, 08:23
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Explanation

Note that a minor arc is the “short way around” the circle from one point to another, and a major arc is the “long way around.” Arc ABC is thus the same as major arc AC.

For a given arc, an inscribed angle is always half the central angle, which would be 80° in this case.

The minor arc AC is thus \(\frac{80}{360}=\frac{2}{9}\)of the circle. Since the circumference is \(36\pi\):

minor arc AC = \(\frac{2}{9}(36\pi) = 8\pi\)

Arc ABC, or major arc AC, is the entire circumference minus the minor arc:

\(36\pi – 8\pi = 28\pi\)
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Re: If the diameter of the circle is 36, what is the length of a   [#permalink] 24 Sep 2018, 08:23
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If the diameter of the circle is 36, what is the length of a

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