Finding three equal segment on two intersecting lines

This is a nice problem I came across. The problem is about two intersecting lines and we have to find two points on these intersecting lines such that the resulting three segments are equal. The idea is to start backward. Think that the problem is already solved and one can see that if we can construct a parallelogram than we can find the solution. To find the parallelogram one needs to use the idea of intercept theorem. We begin with drawing a small isosceles triangle (CDF) and then we we draw a line of equal length (FH) on the side joining CA and then we make use of properties of parallelogram to find the length AJ and then JK is drawn parallel  as shown in the figure below