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# Point Q lies in the interior of a particular circle.

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Point Q lies in the interior of a particular circle.  [#permalink]

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13 Jul 2014, 12:09
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75% (01:00) correct 25% (01:09) wrong based on 461 sessions

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Point Q lies in the interior of a particular circle. Is point Q the center of the circle?

(1) There exist points A, B, and C, all distinct points on the circle’s circumference, such that the distances QA, QB, and QC are identical.

(2) At least two different diameters of the circle contain point Q.

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Point Q lies in the interior of a particular circle.  [#permalink]

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14 Jul 2014, 02:57
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Point Q lies in the interior of a particular circle. Is point Q the center of the circle?

(1) There exist points A, B, and C, all distinct points on the circle’s circumference, such that the distances QA, QB, and QC are identical. Only the center is equidistant from more than two points on the circumference. Hence Q must be the center. Sufficient.

(2) At least two different diameters of the circle contain point Q. Two diameters intersect at the center, hence Q must be the center. Sufficient.

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Re: Point Q lies in the interior of a particular circle.  [#permalink]

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10 Sep 2015, 00:29
Hi Bunuel ,

I got the option one .

But for option 2 i am confused .
(2) At least two different diameters of the circle contain point Q . At least two different diameter means the diameter of different length . Then how come point Q becomes the center of the circle . Please explain . if possible by diagram . Thanks
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Point Q lies in the interior of a particular circle.  [#permalink]

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10 Sep 2015, 01:18
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abhisheknandy08 wrote:
Hi Bunuel ,

I got the option one .

But for option 2 i am confused .
(2) At least two different diameters of the circle contain point Q . At least two different diameter means the diameter of different length . Then how come point Q becomes the center of the circle . Please explain . if possible by diagram . Thanks

The diameter of a circle is the length of the line through the center and touching two points on its edge. The lengths of all possible diameters are the same and different diameters cross each other at the center.

So, if two different diameters have one point in common, then it must be the center.

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Untitled.png [ 2.38 KiB | Viewed 7417 times ]

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Re: Point Q lies in the interior of a particular circle.  [#permalink]

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24 Sep 2016, 01:24
Just wanted to understand - if statement 1 said there exist 2 points instead of 3, this statement would be insufficient right? I am just thinking logically, there can be 2 lines drawn from any point which would be equal ?
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Re: Point Q lies in the interior of a particular circle.  [#permalink]

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26 Sep 2016, 13:37
Neeraj91 wrote:
Just wanted to understand - if statement 1 said there exist 2 points instead of 3, this statement would be insufficient right? I am just thinking logically, there can be 2 lines drawn from any point which would be equal ?

Yes you are right. It has to be equidistant from at least three points.

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Point Q lies in the interior of a particular circle.  [#permalink]

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13 Jan 2017, 10:52
My approach to the problem.

(1) If there are 3 points which lie on the circle's circumference then it must be true that Q is the center of the circle.
Lets test a case in which Q is NOT the center of the circle.

If Q is NOT the center of the circle, located ANYWHERE inside the circle, we CAN draw another circle inside this one in which Q is the center as you can see below.
In this case the new circle can only be tangent at ONE point of the bigger circle's circumference -or even not be tangent at all- , making it IMPOSSIBLE for other points to be equidistant from the center of the new circle to the big circle's circumference.

(2) Every pair of diameters of the circle intersect at only one point inside the circle. The center of the circle.
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Re: Point Q lies in the interior of a particular circle.  [#permalink]

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23 Feb 2017, 05:46
Prompt analysis
Point Q lies inside the circle.

Super set
The answer could be either YES or NO
Translation
We need other information such that we can answer the question based on the property of the circle

Statement analysis
St 1: 3 non collinear points will be equidistant from only one point. If a circle passes through 3 non collinear points,, then the 4 fourth point which will be equidistant from those 3 points will be the centre of the circle.Hence option b,c and e eliminated.

St 2: two diameters intersect at the centre.if the intersection point is q, therefore q is the centre.

Hence option D
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Re: Point Q lies in the interior of a particular circle.  [#permalink]

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21 May 2017, 20:53
WoundedTiger wrote:
Point Q lies in the interior of a particular circle. Is point Q the center of the circle?

(1) There exist points A, B, and C, all distinct points on the circle’s circumference, such that the distances QA, QB, and QC are identical.

(2) At least two different diameters of the circle contain point Q.

Statement 1: An infinite number of points can be equidistant from two points on a circle, but only the center of a circle can be equidistance from more than 2 points. So Q must be the center.

Statement 2: Diameters must pass through the center and they only intersect at the center, so Q must be the center of the circle if two diameters converge there.
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Re: Point Q lies in the interior of a particular circle.  [#permalink]

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29 Jul 2017, 21:48
I have doubt in the statement 2, It says that the point Q is at least on the 2 diameters , so point Q can be on the diameter also. So its not that Q is the center of the circle. Kindly correct me . I know my concept is somewhere incorrect
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Re: Point Q lies in the interior of a particular circle.  [#permalink]

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30 Jul 2017, 01:50
longhaul123 wrote:
I have doubt in the statement 2, It says that the point Q is at least on the 2 diameters , so point Q can be on the diameter also. So its not that Q is the center of the circle. Kindly correct me . I know my concept is somewhere incorrect

What do you mean by the highlighted part?

Two diameters intersect only at one point, at the centre. If Q is on two diameters then it must be the centre. Please re-read the following posts:
https://gmatclub.com/forum/point-q-lies ... l#p1382846
https://gmatclub.com/forum/point-q-lies ... l#p1571862

Hope it helps.
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Re: Point Q lies in the interior of a particular circle.  [#permalink]

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05 Sep 2017, 16:11
WoundedTiger wrote:
Point Q lies in the interior of a particular circle. Is point Q the center of the circle?

(1) There exist points A, B, and C, all distinct points on the circle’s circumference, such that the distances QA, QB, and QC are identical.

(2) At least two different diameters of the circle contain point Q.

Statement 1

This scenario only holds true if each of the lines are equidistant, which can only occur if they branch out from the center of the circle

Statement 2

Bunuel if two lines are not parallel then they intersect right? And in this scenario the lines must clearly intersect at the center?

D
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Re: Point Q lies in the interior of a particular circle.  [#permalink]

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05 Sep 2017, 20:45
Nunuboy1994 wrote:
WoundedTiger wrote:
Point Q lies in the interior of a particular circle. Is point Q the center of the circle?

(1) There exist points A, B, and C, all distinct points on the circle’s circumference, such that the distances QA, QB, and QC are identical.

(2) At least two different diameters of the circle contain point Q.

Statement 1

This scenario only holds true if each of the lines are equidistant, which can only occur if they branch out from the center of the circle

Statement 2

Bunuel if two lines are not parallel then they intersect right? And in this scenario the lines must clearly intersect at the center?

D

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Re: Point Q lies in the interior of a particular circle.  [#permalink]

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28 Sep 2018, 05:05
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Re: Point Q lies in the interior of a particular circle.   [#permalink] 28 Sep 2018, 05:05
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