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.