  Nuclear recoil corrections of order $\alpha^6\,m^2/M$ are calculated for the
lowest-lying triplet states of the helium atom. It improves the theoretical
prediction for the isotope shift of the $2^3S-2^3P$ transition energy and
influences the determination of the ${}^3\textrm{He}-{}^4\textrm{He}$ nuclear
charge radii difference. This calculation is a step forward on the way towards
the direct determination of the charge radius of the helium nucleus from
spectroscopic measurements.
