This is a tip I garnered years ago but as I do not see my CADDies using it. I will share it as a time saver. Works even better in AutoCAD 2009 that in R9 when I first discovered it. Most users, when faced with the need to draw a line on the centerline between two circles that are at a nonperpendicular, will draw a line from centre to centre and then trim it to the edges of a circle. A quick and easy way is to draw a line using the perpendicular command. The sequence is as follows:
Start line with line command.

Pick first point with the perpendicular snap at the edge of first circle (Creates a temporary point which remains perpendicular to first circle as you drag it around.)

Pick second point with perpendicular snap at the edge of second circle.
Now the line is perfectly aligned between the two circles' common centerline.

Notes from Cadalyst Tip Patrol:  Great time-saving tip.  This can reduce eight clicks down to five clicks at most, and three if you are running osnaps set with the perpendicular snap on. Tested in AutoCAD 2009