You can guess that the fastest route through the corner will be the one with the largest radius. We will start with our wheels just touching the outside of the track, turn into the corner so as to just clip the inside kerb halfway through the corner and then unwind back to the outside of the track at the exit. This path is a good approximation to the `racing line'.
If the inner and outer radii of the curve are and , this path has radius
and the driver must start the curve a distance before the actual curve begins.
This just happens to be the position of the first time post in the previous example, and the speed at which the drivers pass it is exactly the maximum cornering speed corresponding to in this example. Driver C, using the racing line, is 0.7 sec faster than driver A. Considering that most races are won by a margin of a few sec, this is a huge advantage. Taking the wrong line is very costly.