  Let $X$ be an isotropic Grassmannian of type $B$, $C$, or $D$. In this paper
we calculate $K$-theoretic Pieri-type triple intersection numbers for $X$: that
is, the sheaf Euler characteristic of the triple intersection of two arbitrary
Schubert varieties and a special Schubert variety in general position. We do
this by determining explicit equations for the projected Richardson variety
corresponding to the two arbitrary Schubert varieties, and show that it is a
complete intersection in projective space. The $K$-theoretic Pieri coefficients
are alternating sums of these triple intersection numbers, and we hope they
will lead to positive Pieri formulas for isotropic Grassmannians.
