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# In the below figure, O is the centre of the circle. What is angle ABC?

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Math Expert
Joined: 02 Sep 2009
Posts: 58335
In the below figure, O is the centre of the circle. What is angle ABC?  [#permalink]

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05 Feb 2019, 22:55
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Difficulty:

55% (hard)

Question Stats:

52% (01:23) correct 48% (01:32) wrong based on 44 sessions

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In the below figure, O is the centre of the circle. What is angle ABC?

(1) Angle OAC = 40 Degrees
(2) Angle AOC = 100 Degrees

Attachment:

Circle.jpg [ 5.97 KiB | Viewed 2146 times ]

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Re: In the below figure, O is the centre of the circle. What is angle ABC?  [#permalink]

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05 Feb 2019, 23:30
2
The sum of the opposite angles of a cyclic quadrilateral is supplementary.

(1) Angle OAC = 40 Degrees
Angle OAC = Angle OCA [radius]
Hence AOC = 100
ABC = 80
Sufficient

(2)AOC = 100
ABC = 80
Sufficient
IMO D
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Re: In the below figure, O is the centre of the circle. What is angle ABC?  [#permalink]

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06 Feb 2019, 04:35
Bunuel wrote:

In the below figure, O is the centre of the circle. What is angle ABC?

(1) Angle OAC = 40 Degrees
(2) Angle AOC = 100 Degrees

Attachment:
Circle.jpg

#1
OA = OC= 40
Angle AOC= 100
central angle = 0.5 of angle subtended on
insribed angle is equal to half of the central angle it intercepts
sufficient
#2
again AOC = 100
so 50= ABC
IMO D
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Joined: 10 Jan 2019
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Re: In the below figure, O is the centre of the circle. What is angle ABC?  [#permalink]

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06 Feb 2019, 05:08
1
1
The inscribed angle ABC should be half of the intercepted arc.
If angle AOC = 100, then intercepted arc is 360 - 100 = 260
Angle ABC is 1/2 * 260 = 130.

Re: In the below figure, O is the centre of the circle. What is angle ABC?   [#permalink] 06 Feb 2019, 05:08
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