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# The point O is the center of the circle circumscribed about triangle A

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Math Expert
Joined: 02 Sep 2009
Posts: 58396
The point O is the center of the circle circumscribed about triangle A  [#permalink]

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26 Mar 2019, 22:57
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Difficulty:

25% (medium)

Question Stats:

94% (00:50) correct 6% (01:13) wrong based on 16 sessions

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The point O is the center of the circle circumscribed about triangle ABC, with angle BOC = 120° and angle AOB = 140°, as shown. What is the degree measure of angle ABC°?

(A) 35
(B) 40
(C) 45
(D) 50
(E) 60

Attachment:

2007_12B_AMC-3.png [ 13.65 KiB | Viewed 415 times ]

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Re: The point O is the center of the circle circumscribed about triangle A  [#permalink]

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26 Mar 2019, 23:03
D
50
Angle AOC = 100
Angle at the circumference should be half of the angle at the centre hence ABC = 50

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Re: The point O is the center of the circle circumscribed about triangle A  [#permalink]

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26 Mar 2019, 23:07
Bunuel wrote:

The point O is the center of the circle circumscribed about triangle ABC, with angle BOC = 120° and angle AOB = 140°, as shown. What is the degree measure of angle ABC°?

(A) 35
(B) 40
(C) 45
(D) 50
(E) 60

Attachment:
2007_12B_AMC-3.png

angle AOC = 360-(140+120) = 100

angle AOC = 2 angle ABC

angle ABC = 100/2 = 50

Hence D
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Re: The point O is the center of the circle circumscribed about triangle A  [#permalink]

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27 Mar 2019, 00:53
Bunuel wrote:

The point O is the center of the circle circumscribed about triangle ABC, with angle BOC = 120° and angle AOB = 140°, as shown. What is the degree measure of angle ABC°?

(A) 35
(B) 40
(C) 45
(D) 50
(E) 60

Attachment:
2007_12B_AMC-3.png

∆ AOB = x=180-140 ; 40 so ABO= 20
and ∆ BOC ; 180-120 ; 60 angle OBC= 30
so angle ABC= 50
IMO D
Re: The point O is the center of the circle circumscribed about triangle A   [#permalink] 27 Mar 2019, 00:53
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