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

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Joined: 02 Sep 2009
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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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11 Sep 2018, 23:33
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Difficulty:

25% (medium)

Question Stats:

83% (00:29) correct 17% (01:12) wrong based on 24 sessions

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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 [ 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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12 Sep 2018, 01:28
Bunuel wrote:

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

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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12 Sep 2018, 06:28
Bunuel wrote:

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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