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In the circle above with center O, what is the measure of angle AOB?

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In the circle above with center O, what is the measure of angle AOB?  [#permalink]

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New post 13 Sep 2018, 01:34
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In the circle above with center O, what is the measure of angle AOB?

(1) The length of the arc AB is π.
(2) The measure of angle ABO is equal to the measure of angle OBC.


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In the circle above with center O, what is the measure of angle AOB?  [#permalink]

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New post Updated on: 14 Sep 2018, 23:35
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Bunuel wrote:
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In the circle above with center O, what is the measure of angle AOB?

(1) The length of the arc AB is π.
(2) The measure of angle ABO is equal to the measure of angle OBC.


Attachment:
image011.gif


Question: what is the measure of angle AOB?

Statement 1: The length of the arc AB is π.

i.e. (Angle AOB/360)*2*π*r = π
But neither do we have angle nor the radius hence nothing can be concluded about the angle ABO hence
NOT SUFFICIENT

Statement 2: he measure of angle ABO is equal to the measure of angle OBC.
While Sum of Angles ABO and OBC = 90º (Property: Any angle on circumference in a semicircle is 90º )
If both angles are equal then each angle must be = 45º
i.e. ABC is an isosceles right angle triangle and OB is perpendicular on AC
i.e. angle AOB = 90º

SUFFICIENT

Answer: option B
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Originally posted by GMATinsight on 13 Sep 2018, 02:05.
Last edited by GMATinsight on 14 Sep 2018, 23:35, edited 2 times in total.
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Re: In the circle above with center O, what is the measure of angle AOB?  [#permalink]

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New post 14 Sep 2018, 09:10
1. Is AOB not a straight line. I think it is the diameter even if it has not been explicitly stated. Consequently, ABC is 90. Am i wrong ?

2. In your explanation how come ABO and OBC sum to be 180 ??

3. Cant we assume that since angle ABC is 90 , the radius OB must bisect ABC. If not, why so. Both the traigles are similar


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Re: In the circle above with center O, what is the measure of angle AOB?  [#permalink]

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New post 14 Sep 2018, 09:28
Hey GMATInsight


Here sum of angle ABO & OBC would be 90 and not 180
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In the circle above with center O, what is the measure of angle AOB?  [#permalink]

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New post 14 Sep 2018, 12:36
(1) The length of the arc AB is = \(Arc Length=π =(Angle of the arc/360°)*Circumference\)-> radius is unknown

(2) The measure of angle ABO is equal to the measure of angle OBC.
In triangle ABO and OBC we have
a) OB is part of both the triangle = common side
b) AO=OC= radius= common side
c) From Statement 2 angle ABO =Angle OBC = angle congruent
SAS triangles are congruent

AC = diameter... If a triangle is inscribed in a circle and has the diameter of the circle as the triangle’s hypotenuse, then that triangle is a right triangle.

so 2*angle ABO=90 ->angle ABO = 45
Angle BAO = Angle ABO = 45
Angle AOB = 90
So B


do correct me if i am wrong. thanks in advance :)
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In the circle above with center O, what is the measure of angle AOB? &nbs [#permalink] 14 Sep 2018, 12:36
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