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This is an imaginary line that denotes the perpendicular line from the travel of the cue ball into the object ball. This line is what the cue will continue along after contact if there is no english, draw, or follow placed on it. With draw it will travel short of this line, and with follow it will travel past this line.
I like to take a long look at the tangent line before taking my shot, so I can get an idea of where the cue ball is going.
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