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The aggro circle, from what I've read and understood, reaches out about 80' (that's feet- using the US standard system).
Short and Half Moon Bows reach 70'.
Flat and Long Bows reach 100'.
Recurve, Composite and Dead bows reach 80'.
The Ithas Bow from EB preorder gets out to 80' as well.
Granted, those aren't the only differences in the bows. They all fire at different speeds and have different accuracies, with Short Bows being the fastest and most accurate, and the others mixed around.
Also, when dealing with bows, you have to take into account that you can't fire another arrow until the one you just shot off hits (the exception being skills like Distracting Shot) so the farther you shoot and, subsequently, the greater the arc the arrow flies in, the longer it's going to take for you to take down life bars. That's one of the reasons skills like Read the Wind are so powerful.
Spellcasting, from what I understand, has a range of 80'. Most monsters won't actually aggro until they're within 75' or so (unless they're attacked, of course), which is why you can cast a spell on a benign enemy before attacking.
Staying at the edge of the range is also the only way a monk can really heal someone tanking an enemy archer or spellcaster without triggering the aggro on themself.
While we're on the subject, Staves and Wands have a range of 80' as well.
Alea Jacta Est - Caesar
I live my life by Murphy's Law.