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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 didn't see it, but there are no answers anyway.2012-11-04
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    Oh no: **there is an answer** debunking the claim. It even has two upvotes.2012-11-04
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    You are wrong. This answer is probably debunking the previous question (it seems to be changed after this answer or something). That image shows, that equity presented in this question is true: $972.02+1222.25+1020.89+770.66=2(972.02+1020.89)$2012-11-04
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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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