Much has been said about tangent line and how it relates to pool. There are some great drills for improving your tangent line which I cover in the article Tangent Line Drill. This article will show you two different systems for getting an accurate tangent line for pure follow and
The first system I will cover is the draw carom. When you're faced with the situation below, the carom is not so easy. If the ball is not centered over the pocket it can be tough to create an exact line to carom in the nine.
This system, when used with very low draw at medium to low speed, can give you a very accurate tangent line. If high speed is necessary, there is an adjustment that can be made, which I will also cover. This is how to line it up:
Make a line (shown in red) from the point of contact on the object ball to the center of where you want the cue ball to finish. Make another line (shown in blue) from the center of the cue ball to the center of the object ball. Imagine a point (shown in green) right in the center of the two lines on the cue ball. The green point is your point of aim for this off angle carom. Medium to low speed is needed to keep the line true, but if you need to hit it hard, the point of aim needs to be a slightly fuller hit on the object ball.
The follow system is a very useful system for caroms as well as safeties. The following system can be used to execute the shot seen below. The one ball doesn't have a pocket, and the seven is nearby. The object is to bank the one out of the way and get the cue ball to creep up under the seven for a lock up safety.
Draw a line (shown in red) from the point where you would like the center of your cue ball to land, and project it back to the object ball. From that point, draw a line back to the cue ball (shown in blue). Aim at that point (shown in green) with very high follow and medium/low speed, and your cue ball should follow right to your target. This one usually takes some practice because most people don't hit their follows high or soft enough. As with the draw shot, a very hard hit requires a slightly fuller hit on the object ball.
Both of these shots can be used in a variety of situations, so when you have safe to play or a carom to make, get creative. Little tricks like these can make a big difference in tough situations.