the number of noncollinear points needed to determine a circle

Two. The location of the center, and one point on the circle (ie, the length of radius), you have determined the circle. However, the circle thus determined can be an an infinite number of planes (not just in the plane of the paper you marked). So if you want the circle in a specific plane, then three points are required.

Generally 3 non-collinear points determine a unique circle.
If you're given 2 you could determine a center and radius, or you could determine the endpoints of a diameter, but I think the question is asking a general question.
Two points incidentally are collinear by definition, so the answer is 3.

yea its defenitly 3

To determine a circle, you need a minimum of three noncollinear points. This means that the points cannot lie on the same straight line.

The reason why three points are required is because a circle is uniquely defined by its center and its radius. By selecting the center and any two points on the circumference of the circle, you can determine the circle's properties. This includes not only the center and radius but also the shape, location, and orientation of the circle.

If you only have two points, they will be collinear, and you can only determine a line segment, not a circle. The two points will give you the endpoints of a diameter or the center and one point, but you won't have enough information to determine the complete circle.

However, it is worth noting that determining a circle with only three points is not sufficient if you want to specify the circle's position in a specific plane. In that case, you would need at least four noncoplanar points to uniquely define the circle's position in three-dimensional space.