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What is the measure of angle AOB in the circle with center O?

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What is the measure of angle AOB in the circle with center O?  [#permalink]

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New post 02 Sep 2018, 22:42
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

70% (01:06) correct 30% (01:11) wrong based on 81 sessions

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Re: What is the measure of angle AOB in the circle with center O?  [#permalink]

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New post 02 Sep 2018, 23:10
B alone is enough to find the minor angle.

1/11 (2. pi.r) = (x° / 360) (2. pi.r)

=> x can be found

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What is the measure of angle AOB in the circle with center O?  [#permalink]

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New post 03 Sep 2018, 08:04
Bunuel wrote:
What is the measure of angle AOB in the circle with center O?

(1) Major arc AB is greater than 180°.
(2) Minor arc AB is 1/11 of the circumference.


Question stem: \(\angle{AOB}\)=?

St1:- Major arc AB is greater than 180°.
Greatest measure of an arc of a circle is the measure of circumference, i.e, \(2\pi*r\)
Given, Major Arc \(AB>\pi\)
So,\(\pi\)<Arc AB <\(2\pi*r\)
No unique value of arc AB as measure of radius is not known and length of arc AB is a variant.
And measure of \(\angle{AOB}\) is dependent on the measure of arc AB.
Therefore, insufficient.

St2:- Minor arc AB is 1/11 of the circumference
Or, Minor Arc AB=\(\frac{2\pi*r}{11}\)
\(\angle{AOB}\) formed by minor arc AB=\(\frac{Arc_{AB}}{Radius}\)=\(\frac{\frac{2\pi*r}{11}}{r}=\frac{2\pi}{11}\)

Sufficient.

Ans. (B)
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Re: What is the measure of angle AOB in the circle with center O?  [#permalink]

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New post 03 Sep 2018, 21:25
1
Bunuel wrote:
What is the measure of angle AOB in the circle with center O?

(1) Major arc AB is greater than 180°.
(2) Minor arc AB is 1/11 of the circumference.

The question is asking a definite value.
1) The information that Major arc is greater than 180° does not give any information which can give definite information about the angle. Hence, insufficient.
2) The arc and angle it forms at the center are directly proportional. For 360°, circumference is 2\(\pi\)r. So, if arc vs circumference ratio is known, angle it is forming at center can be easily calculated. Hence, sufficient.
Hence, B is correct option.
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Re: What is the measure of angle AOB in the circle with center O?  [#permalink]

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New post 10 Nov 2018, 03:38
In this question, angle AOB, is ON major arc or minor arc??

If it's major arc angle will be say towards 360 degree. Whereas AOB is made using minor arc, angle will be towards zero..


Question no where specifies which part of circle is to be used... Hence we have two different angles..

So, E may be correct answer.


If u don't agree with this thought process. Pls mention why..


N if I am making some real mistake while thinking this way.. Pls come to rescue :-)

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Re: What is the measure of angle AOB in the circle with center O?  [#permalink]

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New post 10 Nov 2018, 06:02
GMAT215 wrote:
In this question, angle AOB, is ON major arc or minor arc??

If it's major arc angle will be say towards 360 degree. Whereas AOB is made using minor arc, angle will be towards zero..


Question no where specifies which part of circle is to be used... Hence we have two different angles..

So, E may be correct answer.


If u don't agree with this thought process. Pls mention why..


N if I am making some real mistake while thinking this way.. Pls come to rescue :-)

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Hello

My thoughts on your query are these:

The question doesnt ask specifically about minor angle AOB (less than 180 degrees i mean) or major angle AOB (greater than 180 degrees i mean).
But in any case, from the second statement alone, we would be able to figure out minor angle AOB. If we can figure out minor angle AOB, we can also figure out major angle AOB. So in any case we have our answer with us.

Thats why I think answer should be B.
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Re: What is the measure of angle AOB in the circle with center O?   [#permalink] 10 Nov 2018, 06:02
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