Ranks on the boundaries of secant varieties

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$>b$\mathrm{.}Weproveitprovingthatthe$X$-rank of a general point of the join of $b-2$ copies of $X$ and the tangential variety of $X$ is $>b$.