Let $\alpha(s)$ be a plane curve.
I need to check that the normal line to $\alpha$ at $s$ is orthogonal to the curve that is determined by the centers of curvature on the points in which the curvature of $\alpha$ is maximized or minimized.
I think I could do this if I was actually given the curve, but I can't see any clear way to attack the problem as it stands now.