I stopped back in to see the solution and was amazed to find that as of yet it's still unsolved. After reading through what is known, I think the solution can be figured out from below:
000000000011
123456789112
.....b..l...
Baltimore is the capitol of Maryland.
Lima is the capitol of Peru.
The coordinates Mnemisis posted for circle 9, which is known to be near Peru, plot directly south of Lima, Peru. Which lends me to believe perhaps he was a little off on one of his measurements.
This is further supported by the whole '12 circles to rule them' as capitols rule.
My theory is that every place will be a capitol, and when you take the first letter of each capitol it will give you the code.
We know for a fact circle 6 is Baltimore. The coordinates of Baltimore are 39 10 76 40. Mnemesis measured 39 51 76 14. Pretty close.
For circle 9 he has 19 71 77 33, however, lima is 12 03 77 03. Not so close. Should be more like 12 78. A difference of 5 degrees!
Now we know it's by Peru, so we know he's doing the right thing because his coordinates are by peru, so that confirms his measurements for Baltimore aren't just a cooincidence.
So the huge glaring problem here is this, if the angle measurements are off even a little, then the degrees are going to be off which is going to be a difference of a whole lot on a map.
I don't really care to print it out and measure every angle and then plug the numbers into mapquest ( http://www.mapquest.com/maps/latlong.adp ) in various configurations looking for the closest capitol. But I think if someone does they will have the answer. BTW, unless you figure out a way to tell which is the degree and which is the minute as well as whethere it is + or - then there are a multitude of combinations for each set.