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If the diameter of the circle is 36, what is the length of a
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19 Sep 2018, 17:55
19 Sep 2018, 17:55
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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) \(56\pi\)
Re: If the diameter of the circle is 36, what is the length of a
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20 Sep 2018, 21:56
20 Sep 2018, 21:56
explain how c can be the answer??
Re: If the diameter of the circle is 36, what is the length of a
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24 Sep 2018, 08:23
24 Sep 2018, 08:23
1
Expert Reply
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:
\(36\pi – 8\pi = 28\pi\)
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:
\(36\pi – 8\pi = 28\pi\)
