Data Sufficiency

Hello,

Can you please assist with this:


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.

OA: D


I tried to solve this as follows:

1) My understanding was that Q has to be the center of the circle in-order for the distances QA, QB and QC to be the same. Hence suff.

2) I was not sure if there can be 2 different diameters. I thought that there is only 1 diameter.


Thanks for your help,
Sri

gmattesttaker2 wrote:Hello,

Can you please assist with this:


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.

OA: D


I tried to solve this as follows:

1) My understanding was that Q has to be the center of the circle in-order for the distances QA, QB and QC to be the same. Hence suff.

2) I was not sure if there can be 2 different diameters. I thought that there is only 1 diameter.


Thanks for your help,
Sri

Two diameters of a circle always intersect at the center, hence Q is the center of the circle. There are infinitely many diameters to a circle.

There is one length for the diameter, but you can draw it any number of ways by connecting different points on the circumference through the center of the circle.