Three Congruent Segments on a Given Angle

Given a fixed angle ACB, with the vertex.   

Construct point X on AC and point Y on BC such
that   AX = XY = YB.


HINT:   Most successful constructions use a similar figure. Construct a smaller scale figure where X' is chosen on AC and then construct the similar configuration:

AX'C'Y'B is similar to the desired configuration



See Discussion of   Equal Segments Problem