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08 Jan 2015, 00:32
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
72% (01:34) correct
28%
(01:31)
wrong
based on 94
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Attachment:
2015-01-07_1837.png [ 3.46 KiB | Viewed 9004 times ]
Points A,B,C lie on the circle. Point O is the center of the circle and lies on the line segment AB. If angle COB is 100 degrees then angle CAO equals to
A. 90 degrees
B. 80 degrees
C. 60 degrees
D. 50 degrees
E. 40 degrees
08 Jan 2015, 01:28
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ANS: D
OC & OB are radii, hence triangle OCB is an isosceles triangle.
Angle OCB= Angle OBC
Angle OCB+Angle OBC+ Angle COB = 180
Angle COB = 100
Angle OCB = Angle OBC = (180 - 100) /2 = 40deg
Now, with reference to a theorem which states that any triangle inscribed in a circle with diameter as one of the sides, the opposite angle to diameter is 90 deg.
Therefore angle ACB = 90 deg
ACB = 90, Angle CBA = 40
Hence Angle CAO = 180 - (90+40) = 50 Deg.
OC & OB are radii, hence triangle OCB is an isosceles triangle.
Angle OCB= Angle OBC
Angle OCB+Angle OBC+ Angle COB = 180
Angle COB = 100
Angle OCB = Angle OBC = (180 - 100) /2 = 40deg
Now, with reference to a theorem which states that any triangle inscribed in a circle with diameter as one of the sides, the opposite angle to diameter is 90 deg.
Therefore angle ACB = 90 deg
ACB = 90, Angle CBA = 40
Hence Angle CAO = 180 - (90+40) = 50 Deg.
08 Jan 2015, 14:48
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Hi All,
You don't actually need to figure out the value of big Angle C to answer this question.
We're told that angle COB = 100 degrees.
Since lines add up to 180 degrees, this means that angle COA = 80 degrees
Triangle AOC is ISOSCELES, since OA and OC are both radii of the circle. This means that the two missing angles in that triangle are the SAME.
Triangle AOC = X + X + 80 degrees = 180 degrees
2X + 80 = 180
2X = 100
X = 50 degrees
Angle CAO = 50 degrees
Final Answer:
GMAT assassins aren't born, they're made,
Rich
You don't actually need to figure out the value of big Angle C to answer this question.
We're told that angle COB = 100 degrees.
Since lines add up to 180 degrees, this means that angle COA = 80 degrees
Triangle AOC is ISOSCELES, since OA and OC are both radii of the circle. This means that the two missing angles in that triangle are the SAME.
Triangle AOC = X + X + 80 degrees = 180 degrees
2X + 80 = 180
2X = 100
X = 50 degrees
Angle CAO = 50 degrees
Final Answer:
GMAT assassins aren't born, they're made,
Rich
