Point Q lies in the interior of a particular circle.

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.

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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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.

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

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.

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.

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

________________
Yes, that's correct.

Hi Bunuel,

I chose B, because Q can be equidistant to A, B and C if we draw another circle tangent to the original circle.

Please help

Thanks
Harsh

We are told that A, B, and C are on the circumference of the circle. In your example, A, B, and C cannot simultaneously be on the circumferences of two different circles, because they would have different curvature.

Bunuel, can you elaborate please? My thought process was the same as Harsh's. As far as we are concerned there is only ONE circle, so what's wrong with Harsh sketch? Let's suppose he drew another circle just to prove a point. We can erase the inner circle he drew and keep the points as they are. Doesn't it prove that statement insufficient?

Thanks.

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