  We use nonsmooth critical point theory and the theory of geodesics with
obstacle to show a multiplicity result about orthogonal geodesic chords in a
Riemannian manifold (with boundary) which is homeomorphic to an $N$-disk. This
applies to brake orbits in a potential well of a natural Hamiltonian system,
providing a further step towards the proof of a celebrated conjecture by
Seifert.
