Lets take 3 stretched springs attached to the sides of a triangle (in such a way that they can slip along the lines).  These will be ideal springs with 0 natural length.  Attach all 3 to a mass D, where will it end up?

Press Show to see the geometric answer. (Grey lines are medians, purple lines are angle bisectors, and yellow lines are the reflections of the medians in the angle bisectors.)

Now, can you work out why?