ab and CD are two diameter with the centre and BC and find the measure of all the other angles
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GMAT Club Forum Index Problem Solving (PS)
In the figure AB and CD are two diameters of circle. Interse : Problem Solving (PS)
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Updated on: Dec 4, 2014
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DIFFICULTY: 75% (hard) QUESTION STATS: based on 461 sessions
58% (02:36) correct
42% (02:40) wrong
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In the figure AB and CD are two diameters of circle. Intersecting at angle 48 degree. E is any point on Arc CB. find angle CEB
A. 114
B. 100
C. 80
D. 96
E. 40
Spoiler: OA
Last edited by Bunuel on 04 Dec 2014, 04:32, edited 1 time in total.
Edited the question.
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Most Helpful Community Reply
smyarga
Aug 4, 2014
desaichinmay22 wrote:
smyarga wrote:
Since, CD and AB are two diameters of the circle, so their intersection is the centre. Let's denote this centre O. Angle CEB is inscribed, and angle COB is corresponding central angle (arc CAB). The value of angle COB=180+48=228 degrees. The measure of inscribed angle is always half the measure of the central angle. Angle CEB is equal =228/2=114 degrees.
The correct answer is A.
Hi,
I thought angle COB is 180-42=138 degrees. You have derived angle COB of 228 degrees.
Can you please explain.
That's why I mentioned arc CAB. You don't really need to understand the notions of major and minor arc. Corresponding central angle means that it stays on the same arc as your inscribed angle.