How do I prove that three non-collinear points lie on a circle?
Any three non-collinear points form the vertices of a triangle. Let the Vertices be called A, B, and C.
Any point on the perpendicular bisector of side AB is equidistant from A and B.
Any point on the perpendicular bisector of side AC is equidistant from A and C.
Since the points are not collinear, the perpendicular bisectors intersect.
The point of intersection of the perpendicular bisectors is equidistant from A, and B, and C.
With the point of intersection as the center and its distance from A, or B, or C as the radius, draw a circle.