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Using an estimate on the number of critical points for a Morse-even functionon the sphere $\mathbb S^m$, $m\ge1$, we prove a multiplicity result fororthogonal geodesic chords in Riemannian manifolds with boundary that arediffeomorphic to Euclidean balls. This yields also a multiplicity result forbrake orbits in a potential well.

Functions on the sphere with critical points in pairs and orthogonal geodesic chords