Geodesics avoiding subsets in Hadamard manifolds

Let $M^{n}$, $n\geq 3$, be an $s$-hyperbolic (in the sense of Gromov) Hadamard manifold. Let us assume that we are given a family of disjoint convex subsets and a point $o$ outside these sets. It is shown that if one shrinks these sets by the constant $s$, then it is possible to find a complete geodesic through $o$ that avoids the shrunk sets.