Today I worked for as long as I could on the proposition from yesterday about the inscribed equilateral triangle. I’m feeling a little better, but my mind is still sluggish, so I didn’t make much progress.
I’m wondering whether proving the proposition for a special case first would be helpful. The edge cases where $D$ is the same point as $A$ or $C$ are trivial. The case where $AD = CD$ might provide some insight. On the other hand, using any of the unique characteristics of that case to prove it could leave me as far from a general proof as before.
