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Possible Duplicate:
Proving that $|CA|+|CB|=2|AB|$ in a general $ABC$ triangle

When I was exploring a web collection with geometrical problems I found this one:

How can I prove that in this triangle (image - link) $CA+CB=2AB$?

As shown in image $CD=DE=EB$ and $CF=FE=EA$.

Unfortunately, there was no solution for this. I tried doing it, but I couldn't. Maybe we could use law of sines here? I don't know.

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    Oh, I don't care about that: the answer *supposedly* gives a counterexample to the claim. Whether it *actually* does or not is for whoever's interested to check. I supposed that since it was upvoted it is correct, but perhaps I was mistaken.2012-11-04

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