ExplanationNote 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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