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You said they have to keep the cat in the house...not on the property. Better make up your mind.....perhaps you just want all cats dead huh? J___A__
Unless you can figure out how to tie one up you should keep it in the house, then I will not need to take anymore strays to the pound. Your dog, you can keep on a chain are in a fenced yard. However, have the thing worked on by the vet.