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04 Apr 2018, 23:21
Kudos
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
84% (01:39) correct
16%
(01:35)
wrong
based on 98
sessions
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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. 3π
B. 4π
C. 5π
D. 6π
E. 7π
Attachment:
ArcBC.png [ 7.73 KiB | Viewed 5027 times ]
04 Apr 2018, 23:47
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Bunuel
Given: AOB = 40 degrees; BD = 18 inches
BD is the diameter --> radius = 18/2 = 9 inches.
AOB = 40 degrees, then, BOC (which is holding the minor arc BC in question) = 140 degrees.
Length of the minor arc = (n/360) (2*π*r) --> (140/360) (2*π*9) = 7π
IMO, answer is E.
05 Apr 2018, 06:48
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Bunuel
Attachment:
ArcBCed.png [ 11.24 KiB | Viewed 4401 times ]
Arc BC's central angle measure
as a part of the circle's 360 degrees =
Arc BC's fraction of circumference
• Arc BC's central angle = ?
Arc BC's central angle lies on a straight line with
arc AB's central angle = 40°
So Arc BC's central angle = (180 - 40) = 140°
• Arc BC is what fraction of the circle's circumference?
\(\frac{Part}{Whole}=\frac{140°}{360°}=\frac{14}{36}=\frac{7}{18}\)
• Circumference of circle in inches?
BD = diameter = 18 inches
Circumference = \(\pi d = 18\pi\) in
• Measure, in inches, of arc BC?
Arc BC \(=\frac{7}{18}\) of circumference
\(\frac{7}{18}* 18\pi= 7\pi\)
Answer E
