noncollinear

We begin with the very important notion that any three noncollinear points determine a circle.

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Begin by having your students all draw a triangle with its vertices on a circle (something that is always possible, since any three noncollinear points determine a circle) and then they should select a point on the circle that is not at a vertex of the triangle.

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Marden's theorem, which is set in the complex plane, gives a geometric recipe for finding the exact positions of the roots of p′ when p is a cubic polynomial with distinct noncollinear roots in the complex plane, Kalman said.

MAA Column - Devlin's Angle by Keith Devlin