What is considered "near us" when settling cities?

Sometimes another leader comes sniveling that I am settling cities too close to them. One option is to agree to "stop settling cities so close to us" or something to that effect.

How do I know whether or not settling a particular location will break my agreement? I cannot find any obvious criteria from playing the game, and there is no warning popup when I settle cities.

edit: To clarify, I'm asking about after I agree to "stop settling cities near [them]". What I want to know is where I am permitted to settle a city without breaking the agreement.

Solution 1:

In my experience, If your city is at least 7 tiles away they will not object. 7 tiles is the minimum distance to prevent any overlap in workable tiles, as RhysW mentioned in his comment.

Solution 2:

I've had good luck following the rule that if you can't see any of their tiles from your newly formed city when it's founded, you're fine. In other words, there must be at least two tiles from your new city to any tile within their territory. I wouldn't bet heavily on this being correct, but it's seemed to work for me.