In the circle above, centered on point O, angle AOB measures 40 degrees. If line segment BD measures 18 inches...

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Veritas Prep

In the circle above, centered on point O, angle AOB measures 40 degrees. If line segment BD measures 18 inches, what is the measure, in inches, of minor arc BC?

A. \(3\pi\)
B. \(4\pi\)
C. \(5\pi\)
D. \(6\pi\)
E. \(7\pi\)

OA E

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Veritas Prep

ArcBC.png

In the circle above, centered on point O, angle AOB measures 40 degrees. If line segment BD measures 18 inches, what is the measure, in inches, of minor arc BC?

A. \(3\pi\)
B. \(4\pi\)
C. \(5\pi\)
D. \(6\pi\)
E. \(7\pi\)

OA E

Solution:

Since angle AOB is 40 degrees, angle BOC is 180 - 40 = 140 degrees.

Thus, arc BC is 140/360 = 14/36 = 7/18 of the entire circumference of the circle.

Since the diameter is 18, the circumference is C = πd = 18π.

Thus, arc BC is 18π x 7/18 = 7π.

Answer: E