I know how to trace closed-loop transfer function constant magnitude curves on a Nyquist plot.

I have not yet been able to find a geometric construct to trace closed-loop transfer function constant phase curves. I know these curves are perpendicular to the constant magnitude curves (why?).

Given M a point on the open-loop transfer function, O the origin, and A the point (-1, j0), arg(OM) - arg(AM) = constant should do it. Alas, it leads me nowhere.

Could you give me some tips?

Thank you very much in advance.