If the specific issue is that a tangent line is not precisely tangent, consider using the TAN snap, as Steven suggests. With the OSNAP command, you can set your snaps to stay on permanently. If you're connecting two circles, you can use TAN on both ends of your line to make it doubly tangent.
If you use a snap or FILLET or some other command, you don't have to wonder if your objects connect to each other. Let AutoCAD do the math for you.
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