  Context. Colliding winds in massive binaries are able to accelerate particles
up to relativistic speeds as the result of the interaction between the winds of
the different stellar components. HD 167971 exhibits this phenomenology which
makes it a strong radio source. Aims. We aim at characterizing the morphology
of the radio emission and its dependence on the orbital motion, traced
independently by NIR-interferometry, of the spectroscopic binary and the
tertiary component that conforms HD 167971. Methods. We analyze 2006 and 2016
very long baseline interferometric data at C and X bands. We complement our
analysis with a geometrical model of the wind-wind collision region, and with
an astrometric description of the system. Results. We confirm that the detected
non-thermal radio emission is associated with the wind-wind collision region of
the spectroscopic binary and the tertiary component in HD 167971. The wind-wind
collision region changes orientation in agreement with the orbital motion of
the tertiary around the spectroscopic binary. The total intensity also changes
between the two observing epochs in a way inversely proportional to the
separation between the SB and T, with a negative-steep spectral index typical
of an optically thin synchrotron emission possibly steepened by an inverse
Compton cooling effect. The wind-wind collision bow-shock shape and its
position with respect to the stars indicates that the wind momentum from the
spectroscopic binary is stronger than that of the tertiary. Finally, the
astrometric solution derived for the stellar system and the wind-wind collision
region is consistent with independent Gaia data.
