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.
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