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In the circle above with center O, what is the length of minor arc BC?

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In the circle above with center O, what is the length of minor arc BC? [#permalink]

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New post 15 Jan 2018, 21:53
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A
B
C
D
E

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  35% (medium)

Question Stats:

68% (00:38) correct 32% (00:57) wrong based on 66 sessions

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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
BAC_Circle_O.png [ 11.81 KiB | Viewed 1243 times ]

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Re: In the circle above with center O, what is the length of minor arc BC? [#permalink]

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New post 15 Jan 2018, 22:10
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.

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Re: In the circle above with center O, what is the length of minor arc BC? [#permalink]

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New post 15 Jan 2018, 22:14
Bunuel wrote:
Image
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


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
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Re: In the circle above with center O, what is the length of minor arc BC? [#permalink]

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New post 15 Jan 2018, 22:40
Property used : Any angle cast on circumference of circle which has diameter as base is a 90 degree angle.

[Given] : Value of one angle of triangle ABC i.e 30 degree

[Required] : Length of BC

Solution : Since we have a right triangle ABC, all we need is to apply basic trigonometry to find length of BC.

Both options suggest length of chord. Any one of the option value can be used to find the length of BC.

Hence , option D is the right answer.
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Re: In the circle above with center O, what is the length of minor arc BC?   [#permalink] 15 Jan 2018, 22:40
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