  Context. delta Vel contains the brightest eclipsing binary in the southern
sky (delta Vel A), and a nearby third star located ~0.6" away (delta Vel B).
The proximity of delta Vel B (usable as a reference) makes it a particularly
well-suited target to detect the astrometric displacement of the center of
light of the eclipsing pair. Aims. We obtained NACO astrometric observations
with two goals: (1) to confirm the orientation of the orbital plane of the
eclipsing pair on the sky determined by interferometry (Paper III) and (2)
demonstrate the capabilities of narrow-angle adaptive optics astrometry on a
simple system with predictable astrometric properties. Methods. We measured the
angular separation vector between the eclipsing binary delta Vel A and the
visual companion delta Vel B from narrow-band images at 2.17 microns obtained
with the VLT/NACO adaptive optics system. Based on these observations and our
previous determination of the orbital parameters of the wide binary delta Vel
A-B, we derive the apparent displacement of the center-of-light of the
eclipsing pair at 11 epochs over its orbital cycle. Results. We detect the
astrometric wobble of the center of light of the delta Vel A pair relatively to
B with a typical measurement precision of ~50 microarcseconds per epoch, for a
total amplitude of the measured displacement of ~2 milliarcseconds.
Conclusions. The detected wobble is in agreement with our model presented in
Paper III and confirms the orientation of the Aab orbital plane on the sky. The
residual dispersion compared to our model is 110 microarcseconds rms, that we
tentatively attribute to photometric variability of the fast rotating A-type
components Aa and/or Ab in the BrGamma line. Based on these results, we
conclude that in favorable conditions (bright source with only two resolved
components, small angular separation), narrow-angle astrometry with adaptive
optics on an 8-meter class telescope can reach an accuracy of 50 to 100
microarcseconds.
