1. ## radius of a circle

Referring to the attached pic, work out and present the radius of circle in surd form.

2. 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,
$r^2=x^2+7^2$ ......................(1)
in triangle AFO,
$r^2=(6-x)^2+5^2$ .................(2)

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

\\edit
i got x=1 and radius $r=5 \sqrt{2}$cms