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If O is the center of the circle above, what fraction of the circular
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11 Sep 2012, 03:33
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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 Attachment:
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Re: If O is the center of the circle above, what fraction of the circular
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25 May 2016, 08:38
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. The answer is C.
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Re: If O is the center of the circle above, what fraction of the circular
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11 Sep 2012, 08:56
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 Nonshaded angle = 150 degree Other Nonshaded angle = 150 degree (?) because it is opposite angle Total Nonshaded angle = 150 + 150 = 300 degree So, shaded angle = 360  300 = 60 degree Shaded angle 60  =  = 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 circular
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11 Sep 2012, 08:57
I would say (C), but it seems such an easy answer. Anyways, here is the explanation: 3602*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 circular
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12 Sep 2012, 03:37
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. Hence Answer Choice C.



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Re: If O is the center of the circle above, what fraction of the circular
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12 Sep 2012, 11:57
Fraction of Shaded region = Angle made at the center by shaded region/ Angle at center of a circle = (360150*2)/360 = 60/360 = 1/6 Answer C



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Re: If O is the center of the circle above, what fraction of the circular
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27 Feb 2018, 04:42
dave13 wrote: Bunuel wrote: SOLUTIONIf 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. Answer: C. Kudos points given to everyone with correct solution. Let me know if I missed someone. Hello Bunuel why didnt my simple proporttion method work here 360 = 100% 300 = x The shaded region is 60 degrees not 300.
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Re: If O is the center of the circle above, what fraction of the circular
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11 Sep 2012, 03:34
SOLUTIONIf 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. Answer: C.
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Re: If O is the center of the circle above, what fraction of the circular
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14 Sep 2012, 04:28
SOLUTIONIf 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. Answer: C. Kudos points given to everyone with correct solution. Let me know if I missed someone.
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Re: If O is the center of the circle above, what fraction of the circular
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15 Sep 2012, 07:35
Part of circle not shaded=150+150=300. So, shaded part is 360300=60. 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 circular
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10 Sep 2014, 02:54
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 not shaded is 150+150 =300. so shaded has to be 360300= 60.. 60/360 = 1/6.



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Re: If O is the center of the circle above, what fraction of the circular
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10 May 2016, 17:13
Attached is a visual that should help.
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Screen Shot 20160510 at 5.50.02 PM.png [ 67.54 KiB  Viewed 27300 times ]



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Re: If O is the center of the circle above, what fraction of the circular
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08 Feb 2017, 21:23
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 Answer choice
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Re: If O is the center of the circle above, what fraction of the circular
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08 Feb 2017, 21:57
Non shaded angle = 300 degree.
Shaded angle = 360300 = 60 degree. Fraction = 60/360 = 1/6.
Answer C



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Re: If O is the center of the circle above, what fraction of the circular
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06 Jul 2017, 16:22
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 circular
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13 Nov 2017, 02:49
Bunuel I solved this question using the sector formula. I found this angle method really simple. In what all cases can we use it?



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Re: If O is the center of the circle above, what fraction of the circular
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27 Feb 2018, 03:31
Bunuel wrote: SOLUTIONIf 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. Answer: C. Kudos points given to everyone with correct solution. Let me know if I missed someone. Hello Bunuel why didnt my simple proporttion method work here 360 = 100% 300 = x



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Re: If O is the center of the circle above, what fraction of the circular
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27 Feb 2018, 23:34
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 IMO C whole circle has 360 degree and as opposite angles are equal then opposite angle to 150 is also 150 and unshaded region is 300 shaded region is 60 so area of sector = 60/360pie r^2 which is 1/6pie r^2 and total are is pie r^2 so 1/6pie r^2/ pie r^2 = 1/6



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Re: If O is the center of the circle above, what fraction of the circular
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Re: If O is the center of the circle above, what fraction of the circular
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