Most books present racing cornering in three stages: the approach, where (after braking is completed) the car transitions from an infinite radius (straight) down to the minimum radius for the corner, the middle stage on a constant, minimum radius that (mercifully) ends at the apex, and the exit on an increasing radius, accelerating and tracking out until straight again. This is a nice, neat theory, perhaps first worked out by Piero Taruffi in his book “The Technique of Motor Racing” in 1959. If you think this concept has relevance to autocross racing, best get it out of your head.
As Taruffi goes on to say (after spending many pages working out the geometry of the three stages of every corner) the three-stage method is not the cornering method used by the fast drivers, not even in the 1920’s when he was coming up, much less the 1950’s when he wrote the book and certainly not now in the 2010s. So, put this concept into your head instead: the FAST way through a section of smaller radius has only two stages: Stage 1 is a different type of approach, which ends at the apex, followed by the exit stage as before. The Stage 1 approach is done by turning in later and while traveling faster, then transitioning into a trail-braking slide to scrub off speed, with the path radius constantly getting smaller (and the car slower) until a minimum radius is finally reached at the apex. The second stage, the exit, is done by accelerating on a line of increasing radius just as in the three-stage description. This method allows you to delay your braking and, in fact, to use less braking. Your average speed from turn-in to the apex is higher and the car is pointed better for the exit. It requires a very high degree of car control skill to execute. It requires you to not care about the life of your tires.
I know you want to ask, “Why don’t road-racers corner this way all the time if it’s so fast, Fool?” Probably for two main reasons. Two-stage cornering 1) causes rapid tire wear, and 2) is more prone to error, which is often positively dangerous on a track because an error can easily send you directly off the corner or off on the exit. For road-racers in qualifying, tire wear is no issue, so the fast ones do it. (Somewhat modified this technique is also used to execute passes at corner entry. Fernando Alonso is particularly good at it.) For Time-Trialers going for a fast lap or two per session, tire wear is no issue, so the fast ones do it. For autocrossers, tire wear is a given, there is zero danger, so the fast ones do it.