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

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GRE Prep Club Legend
Joined: 07 Jun 2014
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If the diameter of the circle is 36, what is the length of a [#permalink]  19 Sep 2018, 17:55
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Question Stats:

31% (02:26) correct 68% (00:53) wrong based on 16 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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Intern
Joined: 07 Sep 2018
Posts: 29
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Kudos [?]: 1 [0], given: 5

Re: If the diameter of the circle is 36, what is the length of a [#permalink]  20 Sep 2018, 21:56
explain how c can be the answer??
GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4856
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 102

Kudos [?]: 1731 [0], given: 397

Re: If the diameter of the circle is 36, what is the length of a [#permalink]  24 Sep 2018, 08:23
Expert's post
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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