We have studied HI absorption towards three non-thermal filaments (NTFs) Sgr-C, G359.54+0.18 and G359.79+0.17 using the Giant Metrewave Radio Telescope (GMRT). Our study, for the first time, constrains the distance of the Sgr C NTF and the HII region seen associated with the NTF in the sky plane, to within a few hundred parsecs from the Galactic Centre (GC). A molecular cloud with a velocity of -100 km/s appears to be associated with the central part of the Sgr C NTF. Our study also indicates that the Sgr C HII region is relatively farther away than the NTF along our line of sight, and thereby provides evidence against any possible interaction between the two objects. The NTF G359.54+0.18 shows weak HI absorption (4 sigma detection) at a velocity of -140 km/s, which is the velocity of a known dense molecular cloud seen towards the NTF. This cloud is expected to be located within ~200 pc from the GC and thereby provides a lower limit to the distance. The upper limit to the distance of this NTF from the Sun is 10.5 kpc. The distance to the NTF G359.79+0.17 is between 5.1 and 10.5 kpc from the Sun.
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