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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, 23:42
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Difficulty:

  25% (medium)

Question Stats:

88% (01:01) correct 13% (01:24) wrong based on 32 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 03 Sep 2018, 00:10
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, 09:04
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, 22:25
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? &nbs [#permalink] 03 Sep 2018, 22:25
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