  Let $M$ be a finite volume hyperbolic manifold, we show the equidistribution
in $M$ of the equidistant hypersurfaces to a finite volume totally geodesic
submanifold $C$. We prove a precise asymptotic on the number of geodesic arcs
of lengths at most $t$, that are perpendicular to $C$ and to the boundary of a
cuspidal neighbourhood of $M$. We deduce from it counting results of quadratic
irrationals over $\QQ$ or over imaginary quadratic extensions of $\QQ$, in
given orbits of congruence subgroups of the modular groups.
