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An algorithmic puzzle

Posted on: October 30th, 2013 by
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A Delaunay triangulation of a set of points P in a plane is a partition of the convex hull of P into triangles such that the vertices of each triangle are in P and no point in P lies inside the circumcircle of any triangle of the partition. An example is given below.
Delaunay triangulation

If the set of points P are such that no 4 points lie in a circle, show that the Delaunay triangulation of P is unique.

- via Wikipedia

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