Question

How many circles can be drawn passing through three definite points when they are non collinear?

Answer 1

If given three points which must all lie on the circle, there are two options:

1. The points are collinear… there are zero possible circles containing these points, as circles are not composed of straight lines.
2. The points are non-collinear… there is exactly one unique circle containing these points.

It takes three points to define a curve, and a circle is a special Jordan curve. Thus, it takes three points to define a circle, meaning you can only define one unique circle if given three points.