A simple explanation :
Circumference of a circle = 2 x pi x R
If the TAS = 120 kts/ h, then aircraft is travelling at 2 nm per min.
A rate 1 turn~ 360 degrees in 2 min.
So 2 x pi x R= 4 nm
Therefore R= 4/ (2 x pi)= 2/pi=2/3.14=0.63 nm
which is roughly TAS/200