Is John Conway's proof of Morley's theorem the simplest and free of a deus ex machina? (Q483345)

This paper tries to refute the claim by A. Cain that Conway's proof of Morley's theorem relies on a ``deus ex machina'' (something brought in out of the blue to resolve a situation or disentangle a plot). The author argues that this is not the case and considers Conway's proof (after a small modification) as the simplest know up to date.