Actually if you read the SRD in the section under Attacks of Opportunity you will find the following:
Threatened Squares: You threaten all squares into which you can make a melee attack, even when it is not your action. Generally, that means everything in all squares adjacent to your space (including diagonally). An enemy that takes certain actions while in a threatened square provokes an attack of opportunity from you. If you’re unarmed, you don’t normally threaten any squares and thus can’t make attacks of opportunity.
Reach Weapons: Most creatures of Medium or smaller size have a reach of only 5 feet. This means that they can make melee attacks only against creatures up to 5 feet (1 square) away. However, Small and Medium creatures wielding reach weapons threaten more squares than a typical creature. In addition, most creatures larger than Medium have a natural reach of 10 feet or more.
Provoking an Attack of Opportunity: Two kinds of actions can provoke attacks of opportunity: moving out of a threatened square and performing an action within a threatened square.
It states that you only provoke when you do an action while in a threatened square. And if you do not threaten a square then you can not take an AoO.
In your example with say the disarm or trip, those are reactions that you get when someone attemps those on you and fails.