For a class of dynamical systems, it is shown that trajectories which remain on the boundary of a non-empty, connected subset of a reachable set must be asymptotically stable. Using this result and a reachability maximum principle, we obtain a control law which will drive the system from the origin to the boundary of the reachable set for a class of two-dimensional linear control systems. Using this control law, the reachable set is easily constructed.