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Given 5 points in the plane any three of which are vertices of a triangle. Prove that among these triangles there is an obtuse triangle.

I was able to prove it by examining all possible cases. I would love to see analytical proof though.

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I'm not sure if this is different from examining all cases, but this follows from noticing that any four points don't have an obtuse triangle iff they form a square. –  Karolis Juodelė Nov 24 '12 at 16:41

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