Question

Through any given set of four distinct non-collinear points P, Q, R, S it is possible to draw at most ___circle(s).

Answer 1

Consider two points A and B, infinite number of circles can be drawn passing through them. The one with the least radius is the circle whose diameter is AB. Now consider a point "C" on the plane, only one circle passes through A, B and C. Now if the point D lie on that circle, the answer is one. if the point "D" does not lie on the circle then the answer is zero.
So, at most one circle can be drawn through a given set of four distinct points.