I've thought about this a little, but haven't had time to sit down and work out the math yet. With what's provided, you can easily figure out lengths and angles for everything about triangles OLR and OLD, but that alone doesn't help you.
I suspect the answer lies in using the DC=CH relationship, along with the DE/DF ratio to infer some other relationships. As point C (note Point H moves in relation to point C!) approaches point L, the line DE approaches line DH. As such, the length of DE is important - that length has to change in a very specific way as you move point C along the DH line. This seems to imply that the length of DF is critically important, as it tells you the length of DE... Can we find DF using what we know of triangles OLR and OLD and the relationship the angle FDR has with the length of DC and DH?
Anyways, those are my lunchtime musings... They may lead you towards a solution, or down a blind alley from which there is no return! Either way, it's the journey that matters, not the destination
