A wire of resistance $$R$$ is bent to form a ring. Contacts can be made at points A and B on the ring. A is a fixed contact and B can not be closer to A than a quarter of the perimeter of the ring. Find the maximum and minimum possible resistances between various choices of the contact point B.
[image]

PLACEHOLDER ANSWER - the question has two answers. If the shorter arc is a fraction $$x$$ of the ring, the two arcs $$xR$$ and $$(1 - x)R$$ are in parallel, giving $$x(1 - x)R$$, with $$\frac{1}{4} \le x \le \frac{1}{2}$$. This increases with $$x$$ on that range. So the maximum is $$\frac{R}{4}$$ (B diametrically opposite A) and the minimum is $$\frac{1}{4} \times \frac{3}{4}R = \frac{3R}{16}$$ (B a quarter of the way round).