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# If O is the center of the circle above, what fraction of the

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Math Expert
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If O is the center of the circle above, what fraction of the [#permalink]

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11 Sep 2012, 04:33
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Attachment:

Circle.png [ 7.58 KiB | Viewed 22639 times ]
If O is the center of the circle above, what fraction of the circular region is shaded?

(A) 1/12
(B) 1/9
(C) 1/6
(D) 1/4
(E) 1/3

Practice Questions
Question: 36
Page: 157
Difficulty: 550
[Reveal] Spoiler: OA

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Re: If O is the center of the circle above, what fraction of the [#permalink]

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11 Sep 2012, 04:34
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SOLUTION

If O is the center of the circle above, what fraction of the circular region is shaded?

(A) 1/12
(B) 1/9
(C) 1/6
(D) 1/4
(E) 1/3

150°+150°=300° of the circle is not shaded, hence 360°-300°=60° of the circle is shaded, which is $$\frac{60}{360}=\frac{1}{6}$$ of the circular region.

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Re: If O is the center of the circle above, what fraction of the [#permalink]

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11 Sep 2012, 09:56
1
KUDOS
Bunuel wrote:

Attachment:
Circle.png
If O is the center of the circle above, what fraction of the circular region is shaded?

(A) 1/12
(B) 1/9
(C) 1/6
(D) 1/4
(E) 1/3

Total angle in a circle = 360 degree
One of Non-shaded angle = 150 degree
Other Non-shaded angle = 150 degree (?) because it is opposite angle
Total Non-shaded angle = 150 + 150 = 300 degree
So, shaded angle = 360 - 300 = 60 degree

--------------- = ------- = 1/6
Total angle 360

Hence, C
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Re: If O is the center of the circle above, what fraction of the [#permalink]

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11 Sep 2012, 09:57
1
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I would say (C), but it seems such an easy answer. Anyways, here is the explanation: 360-2*150=60
60 degrees is the total of shaded regions, so 60/360 = 1/6.
So, please correct me if I went awry.

p.s.
where is trick here?
those shaded regions opposite to each other do not have equal angles?
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Re: If O is the center of the circle above, what fraction of the [#permalink]

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12 Sep 2012, 04:37
1
KUDOS
Bunuel wrote:

Attachment:
Circle.png
If O is the center of the circle above, what fraction of the circular region is shaded?

(A) 1/12
(B) 1/9
(C) 1/6
(D) 1/4
(E) 1/3

Since both Lines pass through centers they are alternate angles. Hence shaded degree measure is 360- (150x2)=60

So fraction of circle shaded = 60/360 = 1/6.

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Re: If O is the center of the circle above, what fraction of the [#permalink]

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12 Sep 2012, 12:57
1
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Fraction of Shaded region = Angle made at the center by shaded region/ Angle at center of a circle
= (360-150*2)/360 = 60/360 = 1/6
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Re: If O is the center of the circle above, what fraction of the [#permalink]

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14 Sep 2012, 05:28
SOLUTION

If O is the center of the circle above, what fraction of the circular region is shaded?

(A) 1/12
(B) 1/9
(C) 1/6
(D) 1/4
(E) 1/3

150°+150°=300° of the circle is not shaded, hence 360°-300°=60° of the circle is shaded, which is $$\frac{60}{360}=\frac{1}{6}$$ of the circular region.

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Re: If O is the center of the circle above, what fraction of the [#permalink]

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15 Sep 2012, 08:35
Required fraction is :60/360=1/6
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Re: If O is the center of the circle above, what fraction of the [#permalink]

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10 Sep 2014, 03:54
Bunuel wrote:
Attachment:
Circle.png
If O is the center of the circle above, what fraction of the circular region is shaded?

(A) 1/12
(B) 1/9
(C) 1/6
(D) 1/4
(E) 1/3

Practice Questions
Question: 36
Page: 157
Difficulty: 550

so shaded has to be 360-300= 60..

60/360 = 1/6.

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Re: If O is the center of the circle above, what fraction of the [#permalink]

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04 Feb 2016, 12:56
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Re: If O is the center of the circle above, what fraction of the [#permalink]

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10 May 2016, 18:13
Attached is a visual that should help.
Attachments

Screen Shot 2016-05-10 at 5.50.02 PM.png [ 67.54 KiB | Viewed 9097 times ]

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Re: If O is the center of the circle above, what fraction of the [#permalink]

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25 May 2016, 09:38
1
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Expert's post
Bunuel wrote:
Attachment:
Circle.png
If O is the center of the circle above, what fraction of the circular region is shaded?

(A) 1/12
(B) 1/9
(C) 1/6
(D) 1/4
(E) 1/3

In solving this problem there are three angle rules that we must consider.

1) A circle measures a total of 360 degrees.

2) A straight angle measures 180 degrees.

3) Vertical angles, angles that are directly opposite one another, are always equal.

To solve, we can draw out a quick diagram of just the angles:

Based on the angles we created, we know two important pieces of information:

1) angle A and 150 degrees sum to 180 degrees because they form a straight angle. Thus, angle A = 30 degrees.

2) angle A = angle B because they are vertical angles. Thus angle B = 30 degrees.

With this information we see that the shaded region represents 60 out of 360 degrees of the circle, or 60/360 = 1/6.

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Re: If O is the center of the circle above, what fraction of the [#permalink]

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08 Feb 2017, 22:23
Bunuel wrote:
Attachment:
Circle.png
If O is the center of the circle above, what fraction of the circular region is shaded?

(A) 1/12
(B) 1/9
(C) 1/6
(D) 1/4
(E) 1/3

Practice Questions
Question: 36
Page: 157
Difficulty: 550

Given: The angle opposite the 150 degree angle has the same measure.

Call x = each of of the shaded regions

2(150) + 2x = 360
300 + 2x = 360
2x = 60
x = 30

Sum of the angles of the shaded regions = 60 degrees

60/360 = 1/6

[Reveal] Spoiler:
C

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Re: If O is the center of the circle above, what fraction of the [#permalink]

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08 Feb 2017, 22:57
Non shaded angle = 300 degree.

Shaded angle = 360-300 = 60 degree.
Fraction = 60/360 = 1/6.

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Re: If O is the center of the circle above, what fraction of the [#permalink]

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06 Jul 2017, 17:22
We can also say area of each shaded portion is $$\frac{30*\pi*r^{2}}{360}$$ = $$\frac{\pi*r^{2}}{12}$$
Area of 2 shaded portions = 2 * $$\frac{\pi*r^{2}}{12}$$ = $$\frac{\pi*r^{2}}{6}$$

Ratio is $$\frac{Area of shaded portions}{Area of circle}$$ = $$\frac{1}{6}$$
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Re: If O is the center of the circle above, what fraction of the   [#permalink] 06 Jul 2017, 17:22
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