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15 Jan 2018, 21:53
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
71% (01:16) correct
29%
(01:49)
wrong
based on 127
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In the circle above with center O, what is the length of minor arc BC?
(1) Diameter AC = 24
(2) Chord AB = \(12\sqrt{3}\)
Attachment:
BAC_Circle_O.png [ 11.81 KiB | Viewed 6280 times ]
15 Jan 2018, 22:10
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D
From the figure we can understand that this is 30-60-90 right traingle and the sides AC:AB:BC=2:sqrt(3):1. We need the value of radius (OC) and the angle BOC to find the arc length.
from st1 we get AC=24. Hence OC=12 and BC=12 from the ratio. Hence triangle BOC is equilateral and angle BOC is 60°. sufficient.
from st2 we get AB=12.sqrt(3). Hence from the ratio we get BC=12 and AC=24, OC =12. Hence triangle BOC is equilateral and angle BOC is 60°. sufficient.
Posted from my mobile device
From the figure we can understand that this is 30-60-90 right traingle and the sides AC:AB:BC=2:sqrt(3):1. We need the value of radius (OC) and the angle BOC to find the arc length.
from st1 we get AC=24. Hence OC=12 and BC=12 from the ratio. Hence triangle BOC is equilateral and angle BOC is 60°. sufficient.
from st2 we get AB=12.sqrt(3). Hence from the ratio we get BC=12 and AC=24, OC =12. Hence triangle BOC is equilateral and angle BOC is 60°. sufficient.
Posted from my mobile device
15 Jan 2018, 22:14
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Bunuel
Area of minor arc = 2(Pi)r(center angle/360)
(1) Diameter AC = 24
Angle at the center is twice the Angle at circumference
Center angle = 60
And Also r=12
Hence Suff
(2) Chord AB = \(12\sqrt{3}\)
Join BC & it is 30-60-90
We can find the Diameter & radius
Hence suff
Hence D
