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O is the center point of the circle in the figure

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Carcass
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O is the center point of the circle in the figure [#permalink] New post   25 Dec 2019, 02:10
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#greprepclub O is the center of the circle.jpg
#greprepclub O is the center of the circle.jpg [ 22.39 KiB | Viewed 10285 times ]


O is the center point of the circle in the figure

Quantity A
Quantity B
The length of the minor \(\cap AD\)
The length of the minor \(\cap CB\)



A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

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lindaj616
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Re: O is the center point of the circle in the figure [#permalink] New post   26 Dec 2019, 07:09
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If you draw a line from O to D, you get an isosceles triangle (since OD and OA are the same length).
So, angle OAD = angle ODA (both 65 degrees)
That means, the angle opposite arc AD is 50 degrees (180 - 65 - 65 = 50). So, arc AD > arc CB
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Re: O is the center point of the circle in the figure [#permalink] New post   03 Jan 2020, 20:23
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Join Line OD
OA =OD = Radius of circle
So In triangle OAD
Angle A = Angle D = 65 degree
remaining angle AOD = 50 degree

Angle BOC =40 degree

So the arc will be bigger in A. Hence the answer is A.
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Re: O is the center point of the circle in the figure [#permalink] New post   03 Jan 2020, 20:49
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Carcass wrote:
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The attachment #greprepclub O is the center of the circle.jpg is no longer available


O is the center point of the circle in the figure

Quantity A
Quantity B
The length of the minor \(\cap AD\)
The length of the minor \(\cap CB\)



A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

Kudos for the right answer and explanation


Attachment:
#greprepclub O is the center of the circle.jpg
#greprepclub O is the center of the circle.jpg [ 18.22 KiB | Viewed 10119 times ]


For \(\triangle\) AOB, AO=OD = Radius and

hence the \(\angle\) oad = \(\angle\) oda = 65

therefore central angle = 50

**Greater the central angle, greater is the arc length

central \(\angle\) AOD > central \(\angle\) COB

Hence option A
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Re: O is the center point of the circle in the figure [#permalink] New post   04 Jan 2024, 06:32
Carcass sir, suppose 65 degree is not mentioned in the figure then we would consider angle of arc AD as 40 degree as vertically opposite angle or is there is any condition when two angles can be called vertically opposite ?
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Re: O is the center point of the circle in the figure [#permalink] New post   04 Jan 2024, 09:43
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As you stated in your question, yes we could consider the other angle as 40° but it all depends also on the information in the question or figure
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Re: O is the center point of the circle in the figure [#permalink] New post   28 May 2025, 10:13
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: O is the center point of the circle in the figure [#permalink]
28 May 2025, 10:13
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