  The secant caustic of a planar curve $M$ is the image of the singular set of
the secant map of $M$. We analyse the geometrical properties of the secant
caustic of a planar curve, i.e. the number of branches of the secant caustic,
the parity of the number of cusps and the number of inflexion points in each
branch of this set. In particular, we investigate in detail some of the
geometrical properties of the secant caustic of a rosette, i.e. a smooth
regular oriented closed curve with non-vanishing curvature.
