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rural area equals big territory, but if he has an easy food source, he will probably stick around till there are no resources keeping him there (ie-your chickens are gone)...as much as I hate to say this, as I know it will result in more people choosing to short sightedly kill a problem bobcat rather than give someone the chance to work with it...once a bobcat turns into a chicken killer, it is hard to fix it without removing the cat
I agree. One tied medium sized dog is not enough. These cats are VERY smart. Generally, they do not like to go after prey as large as a chicken, and usually resort to going after things like them and other domestic poultry in lean times but once they discover how wonderful and easy chickens can be, it can be hard to deture them. You would be better off with a large livestock guardian like a pair of anatolian shepherd or great pyranese, but you have to start them young and raise them right to get them to do what you want them to do.
If you decide to trap them, though I absolutely HATE the idea of killing one of these amazing animals (you have NO idea how wonderful, amazing, and INTELLEGENT these creatures are unless you are ever gifted the opportunity to work closely with them in large numbers like I have), because of their large territories, relocating them will most likely not solve your problem, and in all likelyhood will just make them into a problem for someone else.
In your position, I would electrify my fencing, keep my girls penned up for a while, re-enforce everything with heavy gauge wire, and get a couple of LGDs. I have a live and let live motto, and feel it is my responsibility to provide a secure area for my girls. They are prey animals after all. Of course, I am happy to answer any questions you may have. Feel free to PM me if you feel it will help you! I love sharing what little I know about these amazing animals!