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Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  In the figure above, the measure of angle AOB is 120 degrees. If the

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Math Expert V
Joined: 02 Sep 2009
Posts: 58432
In the figure above, the measure of angle AOB is 120 degrees. If the  [#permalink]

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Difficulty:   15% (low)

Question Stats: 87% (02:15) correct 13% (01:57) wrong based on 54 sessions

HideShow timer Statistics In the figure above, the measure of angle AOB is 120 degrees. If the radius of OB is x, then arc AB is what fraction of the area of sector AOB, in terms of x?

A π/x

B √3/x

C 2/x

D 3/x

E 4/x

Attachment: 2019-01-17_1517.png [ 9.6 KiB | Viewed 815 times ]

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Re: In the figure above, the measure of angle AOB is 120 degrees. If the  [#permalink]

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Bunuel wrote: In the figure above, the measure of angle AOB is 120 degrees. If the radius of OB is x, then arc AB is what fraction of the area of sector AOB, in terms of x?

A π/x

B √3/x

C 2/x

D 3/x

E 4/x

Attachment:
2019-01-17_1517.png

Length of arc $$AB=2πx*(\frac{120}{360})=2πx*k$$ (where $$k=\frac{120}{360}$$)

Area of sector $$AOB=πx^2*(\frac{120}{360})$$=$$πx^2*k$$

Now, measure of arc AB: Measure of area of sector AOB=$$2πx*k:πx^2*k$$=$$2:x$$

Ans. (C)
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Manager  G
Joined: 28 Aug 2018
Posts: 226
Re: In the figure above, the measure of angle AOB is 120 degrees. If the  [#permalink]

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Imo C

2/x

2πX 120/360 / πx2 120/360

2/x

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Director  G
Joined: 09 Mar 2018
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Re: In the figure above, the measure of angle AOB is 120 degrees. If the  [#permalink]

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Bunuel wrote: In the figure above, the measure of angle AOB is 120 degrees. If the radius of OB is x, then arc AB is what fraction of the area of sector AOB, in terms of x?

A π/x

B √3/x

C 2/x

D 3/x

E 4/x

Attachment:
2019-01-17_1517.png

Just a quick question, for this figure why are we not considering the outer sector with theta as $$240^o$$

making the answer as E.
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e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3078
In the figure above, the measure of angle AOB is 120 degrees. If the  [#permalink]

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1

Solution

Given:
• Angle AOB = 120 degrees
• Radius, OB = x

To find:
• Length of arc, AB/area of sector AOB

Approach and Working:
• Length of arc, AB = $$\frac{120}{360} * 2ᴨ * x = \frac{2ᴨx}{3}$$
• Area of sector AOB = $$\frac{120}{360} * ᴨ * x^2 = \frac{ᴨx^2}{3}$$

Therefore, the answer is $$\frac{2ᴨx}{3}/\frac{ᴨx^2}{3} = \frac{2}{x}$$

Hence, the correct answer is Option C

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Re: In the figure above, the measure of angle AOB is 120 degrees. If the  [#permalink]

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Bunuel wrote: In the figure above, the measure of angle AOB is 120 degrees. If the radius of OB is x, then arc AB is what fraction of the area of sector AOB, in terms of x?

A π/x

B √3/x

C 2/x

D 3/x

E 4/x

Attachment:
2019-01-17_1517.png

area of sector : 120/360 * pi * x2 and arc AB is 120/360 * 2 * pi * x

ratio would give us
2/x IMO C
Target Test Prep Representative D
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Re: In the figure above, the measure of angle AOB is 120 degrees. If the  [#permalink]

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Bunuel wrote: In the figure above, the measure of angle AOB is 120 degrees. If the radius of OB is x, then arc AB is what fraction of the area of sector AOB, in terms of x?

A π/x

B √3/x

C 2/x

D 3/x

E 4/x

Attachment:
2019-01-17_1517.png

Since the radius is x, the area is πx^2, and since AB corresponds to a 120 degree angle, the area of sector AOB is 120/360 * πx^2 = 1/3 * πx^2 = (πx^2)/3.

Next we determine the circumference of the entire circle and the arclength of arc AB.

Circumference = 2xπ, so arc AB is 120/360 * 2xπ = 1/3 * 2xπ = 2xπ/3.

Finally arc AB is (2xπ/3)/(πx^2/3) = 6xπ/3πx^2 = 2/x of the area of sector AOB.

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Manager  S
Joined: 22 Sep 2018
Posts: 240
Re: In the figure above, the measure of angle AOB is 120 degrees. If the  [#permalink]

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Bunuel wrote: In the figure above, the measure of angle AOB is 120 degrees. If the radius of OB is x, then arc AB is what fraction of the area of sector AOB, in terms of x?

A π/x

B √3/x

C 2/x

D 3/x

E 4/x

If x is the radius that means $$2pi * x$$ is the perimeter and $$x^2 pi$$ is the area

ARC AB is $$\frac{1}{3} of the total perimeter$$ and area of AOB is also $$\frac{1}{3}$$ of the total area.

This means that perimeter : area = (2pi*x/3) : (x^2*pi/3) = $$\frac{2}{x}$$ Re: In the figure above, the measure of angle AOB is 120 degrees. If the   [#permalink] 24 Jan 2019, 13:34
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In the figure above, the measure of angle AOB is 120 degrees. If the

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