Exercise 4, § 7

In the plane $\mathbf{R}^2$, consider the convex set A formed by the points $(\xi, \eta)$ satisfying $-1 \leq \xi \leq 1, -1 - \sqrt{1 - \xi^2} \leq \eta \leq 1 + \sqrt{1 - \xi^2}$. Show that there exist frontier points of A for which the facet is distinct from the intersection of A and of the lines of support of A passing through this point.