How to copy a line segment with a collapsing compass?
Given any line segment BC, how to copy it with point A as the starting point with straight-edge and collapsing compass?
[Hint:
a) Consider the easiest situation: the original segment and the copied one are on the same line
b) Try to move point C to vary the length of the BC, and move point A to vary the distance between A and B. How to relate those lengths together?
c) How about the length of BC > distance between A and B? Vice versa?]