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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
    
What precisely do you mean by analytical? And what cases did you examine? It seems to me that there are many ways you could split this problem into cases. Also, you may find your questions get more answers if you improve your accept rate a little! –  Tom Oldfield Nov 24 '12 at 17:11
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