i makes some modifications for better understanding

given

AB || CD

let distance between center 'O' to CD,OE=x

then ,distance between center 'O' to AB , OF= 6-x (because shortest distance between AB and CD = 6

AF = AB/2 =5 cms and CE = CD/2 = 7 cms.

then using Pythagoras theorem

in triangle CEO,

......................(1)

in triangle AFO,

.................(2)

solve equation (1) and (2)...

\\edit

i got x=1 and radius cms