The cation/anion radius ratio for a triangular arrangement of anions in which the cation is in contact with the anions (but does not push them apart) as shown in the figure is

Explanation

The lines joining the centres of the anions form an equilateral triangle with angle = `60^(@)`
Thus `(b)/(a)= sin 60^(@) = (r_(x))/(r_(x)+r_(M))=0.866`
`:. R_(x)=0.866 r_(x)+0.866 r_(M)`
`0.134 r_(x)=0.866 r_(M)`
`:. (r_(M))/(r_(x))=(0.134)/(0.866) = 0.155`