Why the radius of noble gases is more than the halogens or the previous groups?
Unlike a ball, an atom doesn't have a fixed radius. The radius of atom
  can only be found by measuring the distance between the nuclei of two
  touching atoms and then halving that distance.


According to my findings, I think the reasoning lies in the way in which the measurements are done:



i. Metallic/Covalent radius (left)

ii. Van der Waal radius (right)

It is believed that Noble gases don't form (or rather don't easily form bonds). This way only Van der Waals radius is measured.


The rationale here is based on the fact that noble gases have very low chemical reactivity and their atomic radii are non bonded.
Another explanation lies on electronic configuration of noble gases. They have completely filled outer orbitals with increased repulsion.


In addition, following Hund's rule, in a set of degenerate orbitals, spin-paired electrons exhibit more repulsion compared to singly occupying orbitals which have parallel spins (and consenquently less repulsion).

This also implies that increased electron repulsion between the completely-filled orbitals (as seen in noble gases which all have spin paired electronic configuration) has an effect of increasing "Van der Waals radius" as electrons tend to move as further away as possible to minimise repulsion.

However there is some disparity when comparing Noble gases radii with Group 1 elements (metallic radii) or Halogens (covalent radii) because you are comparing two different unrelated properties,
nevertheless it makes sense to compare radii between different noble gases. 

References


Atomic and Ionic radius
Conceptual Chemistry