I apologise in advance for the horrible phrasing.
If you imagine 3 points like this:
You would then draw a path between A and B and another between B and C, such that the length of the line AB is equal to the line BC. An example of a path is shown below.
Any point of distance "x" along line AB from A can be connected to the point of distance "x" along line BC from B. The straight line distance between these two points would be the same (Distance AB), regardless of the value used for "x".
(Red Line Length = Blue Line Length)
I would like to know if and why this is possible/impossible to construct.