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When it comes to a set of three points, we have a nice theorem that allows us to determine (or prove) whether or not the three points are concyclic. That theorem states the following:
Theorem:
Any three points that are non-collinear (meaning they don't lie on the same line) are concyclic.
This is because if we connect any three non-collinear points with line segments, we form a triangle, and all triangles can be inscribed in a circle.
Three points are trivially concyclic since three noncollinear points determine a circle (i.e., every triangle has a circumcircle).
