SCHWEITZER 1985 Problem 3

Let $k$ and $K$ be concentric circles on the plane, and let $k$ be contained inside $K$ . Assume that $k$ is covered by a finite system of convex angular domains with vertices on $K$ . Prove that the sum of the angles of the domains is not less than the angle under which $k$ can be seen from a point of $K$ . (G.38) [Zs.. Páles]