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

[caralodigiani]

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!

[parthatayi]

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.

[tim]

thanks. caralodigiani, let us know if you need further explanation, and if so please find a way to describe the figure more precisely..

[brentmaster]

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.

[mschwrtz]

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.

[colinkr]

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

[jnelson0612]

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.

[max.h.richards]

Given that Angle BAO = BOA =X, and that those 2 angles also equal OBC and BCO, how is it such that OBC and BCO are 2X while BAO and BOA =x?

[RonPurewal]

Given that Angle BAO = BOA =X, and that those 2 angles also equal OBC and BCO, how is it such that OBC and BCO are 2X while BAO and BOA =x?

You know that AOB and OAB are the same.
Also, separately, you know that OBC and OCB are the same.

There's no reason to think that the measure of the former pair is the same as the measure of the latter pair.
(In fact, it's pretty straightforward to disprove that they're the same: if AOB and OBC were the same, that would make AO and BC into parallel lines. Try drawing it.)

It's like having two different pairs of identical twins. Each pair of twins is the same age, but it's clear that all four of them don't have to be the same age.