Suppose you want to find the relative minor of each major key using the circle. We know that the relative minor is always a minor 3rd down but there's an easier way. Suppose you're in E major on the circle. Take a straight line to the center of the circle then go 90 degrees clockwise to Db (4 o'clock to 7 o'clock). This works with any scale on the circle.

Why not not just count up three positions? Sure. You can do that. But the circle actually shows you the mathematical relationship between notes and scales.