Put faux banner sign down
Count 20 tiles in every direction from it (not including original tile), wherever it ends is the end of the tile.
For example:

Crudely drawn, but I think it should show the general idea. Blue is where banners go, this is how you should do it when expanding to get the most out of your space, or so I've seen, the corners handle the offset, there are a few times when a river will be in the way, just get as close to the corner as possible, a corner will allow most of the new banner's coverage to fall outside the original's range.
In your example of already having area claimed where you're going, it's up to you, but the banner only needs to cover what tile it's on, not go one tile back. If you're looking at breaking old banners for the least banners overall coverage, I'd advise against it, there is no reason to break banners, they provide you with authority, which it's always nice to have more of, and the more banners you have the higher your Days:Authority ratio lasts until it hits a certain point.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . .Hi. . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .