Segment f: Segment A,B
Line g: Line through B perpendicular to f
Point C: Point on g
Point C': C mirrored at f
Segment h: Segment A,C
Point D: Midpoint of h
Segment i: Segment C',D
Point E: Intersection of f and i
Point B': B mirrored at E

Points in de segment: A, B', E and B.