First off, the formula for motion in a circle, R = Vsqu/A refers to acceleration toward the centre, A.

 

In a level turn, there are two accelerations acting on the aircraft, g and N. N is acceleration in the aircraft vertical, aka Load Factor. Because the aircraft is banked N is factored into one g vertically to hold the aircraft level, and A, the acceleration toward the centre. From the normal diagram you can see that geometrically, Tan AOB is A/g, so A = gTan AOB, and R = Vsqu/gTan AOB. Pure geometry! The diagram in our notes labels the arrows as forces (weight, Lift and CPforce), but the aircraft mass is determined, so acceleration and force are equivalent.

 

It is now a second stage to find LF. Again, purely geometrically, N, or Load Factor is 1(g)/cos AOB