The statement provided is correct. When three non-collinear points are given, they can be used to form a unique circle. The center of this circle is the point of concurrency of the perpendicular bisectors of the line segments joining the three points.
Here's an explanation of the process:
1. Consider three non-collinear points: A, B, and C.
2. Construct the line segments AB, BC, and AC.
3. Find the midpoint of each line segment (AB, BC, and AC). These midpoints are the points where the perpendicular bisectors intersect.
4. Construct the perpendicular bisector for each line segment. The perpendicular bisector is a line that is perpendicular to the line segment and passes through its midpoint.
5. The point of concurrency is the point where all three perpendicular bisectors intersect. This point will be the center of the circle.
6. The circle passing through points A, B, and C can be drawn using the center point obtained in step 5 and any of the three points.
This construction guarantees that all three points lie on the circumference of the circle, and the center of the circle is the point of concurrency of the perpendicular bisectors.
Therefore, any three non-collinear points can be used to determine a unique circle, with its center as the point of concurrency of the perpendicular bisectors of the line segments joining the points