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# Point O is the center of the semicircle. If ∠ BCO = 30 ° and

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Point O is the center of the semicircle. If ∠ BCO = 30 ° and [#permalink]  30 Nov 2018, 17:25
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Point O is the center of the semicircle. If ∠ BCO = 30 ° and $$BC = 6 \sqrt{3}$$ what is the area of triangle ABO?

Attachment:

GRE exam - Point O is the center of the semicircle..jpg [ 9.5 KiB | Viewed 1475 times ]

A. $$4 \sqrt{3}$$

B. $$6 \sqrt{3}$$

C. $$9 \sqrt{3}$$

D. $$12 \sqrt{3}$$

E. $$24 \sqrt{3}$$
[Reveal] Spoiler: OA

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Last edited by Carcass on 03 Dec 2018, 11:13, edited 1 time in total.
Edited by Carcass
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Re: Point O is the center of the semicircle. If ∠ BCO = 30 ° and [#permalink]  03 Dec 2018, 10:54
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Missing information from the prompt.

Should state: BC = 6√3
Founder
Joined: 18 Apr 2015
Posts: 6647
Followers: 107

Kudos [?]: 1275 [0], given: 6017

Re: Point O is the center of the semicircle. If ∠ BCO = 30 ° and [#permalink]  03 Dec 2018, 11:14
Expert's post
Thank you so much. Did not show up.

Regards
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Re: Point O is the center of the semicircle. If ∠ BCO = 30 ° and [#permalink]  03 Dec 2018, 19:26
Expert's post
Carcass wrote:
Point O is the center of the semicircle. If ∠ BCO = 30 ° and $$BC = 6 \sqrt{3}$$ what is the area of triangle ABO?

Attachment:
GRE exam - Point O is the center of the semicircle..jpg

A. $$4 \sqrt{3}$$

B. $$6 \sqrt{3}$$

C. $$9 \sqrt{3}$$

D. $$12 \sqrt{3}$$

E. $$24 \sqrt{3}$$

triangle ABC is a right angled triangle at A, and ∠ BCO = 30 °, so ABC is 30-60-90 triangle and sides are in ratio 1:$$\sqrt{3}$$:2
now opposite 60 is side $$BC = 6 \sqrt{3}$$, so AB=6 and AC=12=2*radius.... radius = 6

Let us see OAB..
As we can see AB=6 and OA=OB=radius=6
so it is an equilateral triangle with side 6..
area = $$(\sqrt{3}/4)*6^2=9\sqrt{3}$$

C
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Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

Re: Point O is the center of the semicircle. If ∠ BCO = 30 ° and   [#permalink] 03 Dec 2018, 19:26
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