  In many cases (e.g. for many Segre or Segre embeddings of multiprojective
spaces) we prove that a hypersurface of the $b$-secant variety of $X\subset
\mathbb {P}^r$ has $X$-rank $>b$. We prove it proving that the $X$-rank of a
general point of the join of $b-2$ copies of $X$ and the tangential variety of
$X$ is $>b$.
