what is the number of noncollinear points that determine a cirlce
infinite
The minimum number of noncollinear points that will determine a unique circle is 3.
To understand why 3 noncollinear points determine a unique circle, we need to understand what it means for points to be noncollinear, as well as how circles are defined.
In geometry, collinear points are points that lie on the same straight line. Noncollinear points, therefore, are points that do not lie on the same straight line.
A circle, on the other hand, is a set of points in a plane that are equidistant from a fixed point called the center. The distance from any point on the circle to the center is called the radius.
Now, let's consider the 3 noncollinear points needed to determine a circle. If we have three such points, we can draw three different lines connecting each pair of points. The three lines will never be parallel, as they are formed by connecting noncollinear points. In fact, they will intersect at a unique point, which we can consider as the center of the circle.
Next, we need to determine the radius. For any one of the three points, we can measure the distance from that point to the center. This distance will be the same for all three points, as they lie on the circumference of the circle. Therefore, we can determine a unique circle with a fixed center and radius using these three noncollinear points.
In summary, 3 noncollinear points are the minimum number required to determine a unique circle. These three points allow us to determine the center and radius of the circle, which uniquely define its shape and position in the plane.