First of all thanks to everyone who took time to read and consider this problem in order to help me out, I appreciate it.
So I have a method to prove the claim. I'll sketch the ideas that lead to the proof quickly right now for this who are interested and post something more detailed when I...
Homework Statement
let f: J --> R^2 be a unit speed curve curve and define it's tangentially equidistant campanion by g(u) = f(t) + r*f'(t) for a fixed r>0. Show that the centre of the osculating circle of f at some u in J is the intersection of the line normal to f'(u) through f(u) and the...