Drawing a line to a middle of an object

Hello,
Mainly for drawing block diagrams, but also for other cases, I would like to draw a line that goes to the middle of a boundary of, e.g., a rectangular box or the middle of a line. Another case is drawing a circle the center of which is the middle of a line or the middle of one of the boundaries of a box. The snapping options (vertex, boundary, intersection) don't help. Clearly if I use grid and draw everything "symmetric" to that grid, I could find the middle of lines. But what if I don't go with the grid, or if an object was moved from the grid due to, e.g., alignment operations?
To sum up, I am looking for a way to find the middle of a boundary of a rectangle or a line segment.
Thanks,
Moshe