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In the figure shown, point O is the center of the semicircle

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caralodigiani
 Post subject: In the figure shown, point O is the center of the semicircle
 Post Posted: Sun Sep 19, 2010 7:40 pm 
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Posts: 4
GMAT PREP - CAT #2 - Data Sufficiency

In the figure shown, point O is the center of the semicircle and points B, C, and D lie on the semicircle. If the length of the line segment AB is equal to the length of OC, what is the measurement of angle BAO?

(1) Angle COD= 60 degrees
(2) Angle BCO= 40 degrees

(Cannot paste image, but it is a semi-circle with an inscribed triangle)

Thank you!
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parthatayi
 Post subject: Re: In the figure shown, point O is the center of the semicircle
 Post Posted: Mon Sep 20, 2010 12:36 am 
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Course Students


Posts: 40
caralodigiani wrote:
GMAT PREP - CAT #2 - Data Sufficiency

In the figure shown, point O is the center of the semicircle and points B, C, and D lie on the semicircle. If the length of the line segment AB is equal to the length of OC, what is the measurement of angle BAO?

(1) Angle COD= 60 degrees
(2) Angle BCO= 40 degrees

(Cannot paste image, but it is a semi-circle with an inscribed triangle)

Thank you!


Consider the triangles ABO and BOC,
Angle BAO = BOA =OBC=BCO are equal
OB is the common side for both the triangles.
Hence triangles ABO and BOC are similar

Similarly OBC and COD are similar.

Consider statement (1)
We know Angle COD=60
=> angle ODC=60
=>angle BAO=60

Consider statement (2)
Angle BCO= 40 degrees
As triangles ABO and BOC are similar
Angle BAO=Angle BCO.

Hence OA is D

Thanks and Regards,
Partha.
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tim
 Post subject: Re: In the figure shown, point O is the center of the semicircle
 Post Posted: Sat Sep 25, 2010 7:02 am 
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ManhattanGMAT Staff


Posts: 2242
Location: Southwest Airlines, seat 21C
thanks. caralodigiani, let us know if you need further explanation, and if so please find a way to describe the figure more precisely..

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Tim Sanders
Manhattan GMAT Instructor
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brentmaster
 Post subject: Re: In the figure shown, point O is the center of the semicircle
 Post Posted: Sun Oct 17, 2010 12:11 am 
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Students


Posts: 1
parthatayi, I agree with your answer choice but am confused about how your provided explanation is correct.
stmt 1 bao =60
stmt 2 bao = 40
This shouldn't be possible. Also, BAO doesn't actually equal 60 or 40 for either solution.

Regarding statement 1
"We know Angle COD=60
=> angle ODC=60
=>angle BAO=60"
Using this logic, angle BCO would have no value. If it were 0 then this answer would be correct.
I found this earlier today and felt foolish for not coming up with the same solution.
http://www.postimage.org/image.php?v=Pq12R9Vi

Regarding statement 2
BCO = 40
=> OBC = 40
=> ABO = 180-40 = 140
=> BAO = (180-140)/2 = 20

I hope that is some what intelligible, kind of difficult to explain without visuals.
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mschwrtz
 Post subject: Re: In the figure shown, point O is the center of the semicircle
 Post Posted: Tue Oct 19, 2010 3:29 pm 
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ManhattanGMAT Staff


Posts: 506
Thanks for the link brentmaster. I assume that this is your own work, rather than an image captured from the question? I ask because it doesn't quite match the description offered by the TS.

Your solution is quite clever for the question you illustrated.
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colinkr
 Post subject: Re: In the figure shown, point O is the center of the semicircle
 Post Posted: Mon Nov 15, 2010 8:39 pm 
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Students


Posts: 1
I like the solution provided.
However, are we certain from the information provided that AC is a straight line?
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jnelson0612
 Post subject: Re: In the figure shown, point O is the center of the semicircle
 Post Posted: Sat Nov 20, 2010 9:10 pm 
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ManhattanGMAT Staff


Posts: 1857
colinkr wrote:
I like the solution provided.
However, are we certain from the information provided that AC is a straight line?


colinkr, you can generally assume that the distance between two points in a GMAT geometry problem is the shortest possible path, or a straight line.

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Jamie Nelson
ManhattanGMAT Instructor
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