So basically the most accurate approach that is near something practical is using arbitrary precision. What I was wondering is if there is any implementation capable of detecting for example that the three bisectors of a triangle meet exactly at the same point, the incenter. My guess is that maybe for pedagogical purposes but not for anything more complex.
The problem is that once you start dealing with the actual coordinates of intersections, you have to start picking what properties you wish to keep and which you wish to abandon. Things like parallelism, inside vs outside, winding, handedness, etc. often get very murky once you start dealing with finite precision.
