Given:
A,B, and N are collinear and AB+BN= AN.
To find:
The point which is between the other two points.
Solution:
If A,B, and N are collinear, then these three points must be lie a single straight line.
AB + BN = AN
It means, the segment AN is the addition of two small segments AB and BN.
Using segment addition property, it is possible it and only if point B lies between A and N.
Therefore, the point B lies between A and N.