>alexb,
>
>equations and crank. Oh well.

Thank you for posting here. They both are truly nice problems.
The second one combines quantities that I never before even saw used. But it is pretty simple.

Configuration of the first one admits a generalization that I placed at

http://cut-the-knot.org/Curriculum/Geometry/Markowsky2.shtml

I expect there to be some generalization anglewise, perhaps for a different direction. I am away right now. Will be looking into that when back.

Alex