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

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In the figure shown, point O is the center of the semicircle [#permalink] New post 04 Oct 2009, 22:22
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A
B
C
D
E

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  45% (medium)

Question Stats:

61% (02:42) correct 39% (01:32) wrong based on 46 sessions
OPEN DISCUSSION OF THIS QUESTION IS HERE: in-the-figure-shown-point-o-is-the-center-of-the-semicircle-89662.html
[Reveal] Spoiler: OA

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Re: Geometry (Semicircle, Triangle) from GMATPrep [#permalink] New post 05 Oct 2009, 05:26
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Editing: (statement says <COD=60 and in my calculation I mistaken it for <COB)

Write down everything you know from the Q:
BO=CO=r=AB --> BOC and ABO are isosceles.
<BAO=<BOA and <BCO=<OBC
<CBO=2<BAO

(1) <BAO +<ACO=<COD=60 degrees (Using exterior angle theorem)
<ACO = <CBO = 2<BAO
So, <BAO + <ACO = 2<BAO + <BOA = 3* (<BAO) = 60 degrees
<BAO = 20 degrees SUFFICIENT

(2) <BCO=40 degrees --> <BCO=<CBO=40 degrees=2<BAO --> <BAO=20 degrees. SUFFICIENT

D.
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Last edited by Bunuel on 05 Oct 2009, 11:28, edited 1 time in total.
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Re: Geometry (Semicircle, Triangle) from GMATPrep [#permalink] New post 05 Oct 2009, 08:34
OB = OC = AB = OD.So each statement alone is suff.

I wud go with option D
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Re: Geometry (Semicircle, Triangle) from GMATPrep [#permalink] New post 05 Oct 2009, 11:39
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Last edited by Bunuel on 07 Oct 2009, 14:32, edited 1 time in total.
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Re: Geometry (Semicircle, Triangle) from GMATPrep [#permalink] New post 07 Oct 2009, 13:48
deepakraam wrote:
OB = OC = AB = OD.So each statement alone is suff.

I wud go with option D


Can you please explain how you came up with option D just by stating OB = OC = AB = OD. :roll: I spent nearly 5 min to decide that ans is D.
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Re: Geometry (Semicircle, Triangle) from GMATPrep [#permalink] New post 21 Apr 2010, 06:43
Imagining the shapes visually might prove to be another way of doing this.

The question translates into - Is there only ONE possible line that satisfies the given figure spatially.
(1) When \angle COD is fixed, there can be many lines possibly drawn from C to A, but only one line would render length AB = radius
(2) When \angle BCO is fixed, the same reasoning applies.

So now we know that in either of the cases, we CAN zero down to one particular line segment, wich means that \angle BAO is fixed (whatever it be). So answer is D.
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Re: Geometry (Semicircle, Triangle) from GMATPrep [#permalink] New post 17 Jan 2013, 06:03
Can some1 help me in explaining how do we get <CBO=2<BAO.I really dont uderstand how they derive this.Can someone shed some light on this?
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Re: Geometry (Semicircle, Triangle) from GMATPrep [#permalink] New post 17 Jan 2013, 06:22
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skamal7 wrote:
Can some1 help me in explaining how do we get <CBO=2<BAO.I really dont uderstand how they derive this.Can someone shed some light on this?


Check here: in-the-figure-shown-point-o-is-the-center-of-the-semicircle-89662.html#p664937

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Geometry (Semicircle, Triangle) from GMATPrep   [#permalink] 17 Jan 2013, 06:22
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