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If the angle BAC has a measure of 30°, and the radius of the circle sh

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If the angle BAC has a measure of 30°, and the radius of the circle sh  [#permalink]

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New post 11 Sep 2018, 23:33
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If the angle BAC has a measure of 30°, and the radius of the circle shown above with center O is 8, what is the length of BC?


A. \(8\sqrt{3}\)

B. \(8\sqrt{2}\)

C. 8

D. \(4\sqrt{3}\)

E. \(4\sqrt{2}\)


Attachment:
image018.jpg
image018.jpg [ 2.58 KiB | Viewed 364 times ]

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Re: If the angle BAC has a measure of 30°, and the radius of the circle sh  [#permalink]

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New post 12 Sep 2018, 01:28
Bunuel wrote:
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If the angle BAC has a measure of 30°, and the radius of the circle shown above with center O is 8, what is the length of BC?


A. \(8\sqrt{3}\)

B. \(8\sqrt{2}\)

C. 8

D. \(4\sqrt{3}\)

E. \(4\sqrt{2}\)

angle BOC= 2*angle BAC

angle BOC=60

BO=OC=radius

hence 180-2x-60

hence OBC=OCB=60

Hence it is equilateral triangle hence BC=8

Hence C


Attachment:
image018.jpg

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Re: If the angle BAC has a measure of 30°, and the radius of the circle sh  [#permalink]

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New post 12 Sep 2018, 06:28
Bunuel wrote:
Image
If the angle BAC has a measure of 30°, and the radius of the circle shown above with center O is 8, what is the length of BC?


A. \(8\sqrt{3}\)

B. \(8\sqrt{2}\)

C. 8

D. \(4\sqrt{3}\)

E. \(4\sqrt{2}\)


Attachment:
image018.jpg

\(∠BOC = 2∠BAC = 60°\)

\(△BOC\) = Equilateral Triangle as \(BO = OC\) = Radius of the circle & Each Angles of the Triangle are \(60°\)

Thus, length of BC = 8, Answer must be (C)
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Re: If the angle BAC has a measure of 30°, and the radius of the circle sh &nbs [#permalink] 12 Sep 2018, 06:28
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