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.

Question

01-10-2019
Mathematics

contestada

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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Answer:

Yes, Q is the center of the circle

Step-by-step explanation:

To answer this we need to know what is a circle and some of its components:

(1) The circumference is a curved line of equidistant points to a point Q called center. There is infinitive equidistante points.

(2) The diameter is any segment that joins 2 points of the circumference through the center.

So, if there are points A, B and such that the distances QA,QB and QC are identical, (1) and at least 2 different diameters of the circle contain point Q (2), then, point Q is the center.