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If O is the center of the circle above and the length of chord AB is 2

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If O is the center of the circle above and the length of chord AB is 2 [#permalink]

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New post 29 May 2017, 10:02
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Difficulty:

  95% (hard)

Question Stats:

34% (01:08) correct 66% (02:06) wrong based on 71 sessions

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If O is the center of the circle above and the length of chord AB is 2 units, what is the length of the arc ACB?

(1) The area of ΔOAB is \(\sqrt{3}\) square units
(2) The area of sector OACBO is \(\frac{2π}{3}\)
[Reveal] Spoiler: OA

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Re: If O is the center of the circle above and the length of chord AB is 2 [#permalink]

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New post 29 May 2017, 11:04
The length of the chord :2 UNITS

For some of the questions my strategy is to look at the answer choices.

Lets look at Statement 1 The area of OAB is √ 3

If you remember by far the most common occurrence of √3 on the GMAT is via a 30-60-90, or an equilateral triangle

Area of equilateral triangle is S^2√3/4 So to get the area of √3 . S(Side) has to be 2. Each angle of equilateral triangle is 60 degree.

OA=AB=OB = 2 units (Radii)
To find the length of arc Central angle/ 360 * Circumference. 60/360*4pi =2/3pi

So A is sufficient

Now lets look into Statement 2

Area of sector = Central angle/ 360 * Area of Circle

From statement 2 Area of sector is 2pi /3

Central Angle/360 * Pi r^2= 2pi/3

I have 2 variables and No way to identify either angle or radii.

So Statement D is insufficient.

Answer is A.

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Re: If O is the center of the circle above and the length of chord AB is 2 [#permalink]

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Statement 1 by itself is enough
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Re: If O is the center of the circle above and the length of chord AB is 2 [#permalink]

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New post 02 Dec 2017, 18:58
Please see my explanation


chesstitans wrote:
so, the trap here is in st 2, the sector, not the quadrilateral, has the area.

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Re: If O is the center of the circle above and the length of chord AB is 2   [#permalink] 02 Dec 2017, 18:58
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If O is the center of the circle above and the length of chord AB is 2

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