The circle of traction is a important racing concept with applications from physics. From newtons equation f=ma we know that the more force we apply to an object of constant mass (the car) it will accelerate faster.  Since the car moves in two dimensions its accelerations are in vector form.  If we are going to keep the tires from sliding, the sum of the acceleration and turning vector's magnitude can't be larger then the max force of our tires.  This max force of traction forms a circle, with the radius forming a circle.  (Chassis Engineering) You can see why if your on the brakes you have less traction for turning.   We know this from real life too, since if you have a really tight turn in a car, if you slam your breaks your going to slide off at a tangent to the curve.