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I'm trying to prove that the convex hull of a set X of three or more points in the plane is the union of all the triangles determined by triples of points from X, however I can't think of the meaningful approach to go with. And now I'm really interested what kind of theorems or rules would explain how is the convex hull a union of all the triangles determined by triples of points from X.

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  • $\begingroup$ If $C$ is that convex hull and $T$ is the union of those triangles, you need to prove that $C\subseteq T$ and $T\subseteq C$. Have you tried either proof? To work with this problem you need to know the rigorous definition of the convex hull of a set; do you know it? $\endgroup$ – Greg Martin Nov 4 '19 at 16:44
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(1) Every triangle must be a subset of the convex hull. (2) Suppose some edge of the convex hull doesn't belong to any triangle -> contradiction.

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