The Tangent Line
The natural right-angle path a stunned cue ball takes off the object ball, and how to use it.
What the tangent line is
When a cue ball with no spin (or in a pure stun state) strikes an object ball, the cue ball's natural path after contact runs roughly ninety degrees from the object ball's direction of travel — this ninety-degree line is called the tangent line. It is one of the most reliable rules of thumb in position play because it holds true across a wide range of cut angles.
Follow and draw bend the path off the tangent
Topspin (follow) curves the cue ball's path forward, away from the tangent line and further in the direction of the shot; backspin (draw) curves it backward, away from the tangent line and back toward where the cue ball came from. Reading the tangent line first, then judging how much follow or draw will bend you off it, is how experienced players predict where the cue ball will finish.
Using the tangent line to plan position
Before choosing your speed and spin, trace the tangent line off the object ball to see where a pure stun shot would send the cue ball, then decide whether you need to bend forward off that line with follow or pull back off it with draw to reach your next shot. This two-step process — find the tangent, then adjust — turns a complex three-dimensional problem into a simple, repeatable routine.