  We study the intersection numbers defined on twisted homology or cohomology
groups that are associated with hypergeometric integrals corresponding to
degenerate hyperplane arrangements in the projective $k$-space. We present
formulas to evaluate the intersection numbers in the case when exactly one
$(k+1)$-tuple of the hyperplanes intersects at a point. As an application, we
discuss the contiguity relations of hypergeometric functions in terms of the
intersection numbers on twisted cohomology groups.
