  We analysed 30 RR Lyrae stars (RRLs) located in the Large Magellanic Cloud
(LMC) globular cluster Reticulum that were observed in the 3.6 and 4.5 $\mu$m
passbands with the Infrared Array Camera (IRAC) on board of the Spitzer Space
Telescope. We derived new mid-infrared (MIR) period-luminosity PL relations.
The zero points of the PL relations were estimated using the trigonometric
parallaxes of five bright Milky Way (MW) RRLs measured with the Hubble Space
Telescope (HST) and, as an alternative, we used the trigonometric parallaxes
published in the first Gaia data release (DR1) which were obtained as part of
the Tycho-Gaia Astrometric Solution (TGAS) and the parallaxes of the same stars
released with the second Gaia data release (DR2). We determined the distance to
Reticulum using our new MIR PL relations and found that distances calibrated on
the TGAS and DR2 parallaxes are in a good agreement and, generally, smaller
than distances based on the HST parallaxes, although they are still consistent
within the respective errors. We conclude that Reticulum is located ~3 kpc
closer to us than the barycentre of the LMC.
