Ok, so we need to find the conditions that are required for the bicycle to stay on the track at

.

They are that the centripetal force supplied by the loop (

) needs to be greater than

.

The initial energy of the system is all gravitational potential which is

and at part

this energy is transformed into some kinetic (note that some potential still remains)

;

(where

is the minimum speed required to stay on the loop)

solving

=>

subbing in

in terms of

;

Total Energy required to complete loop in terms of

;

Since energy is conserved we can equate the initial gravitational potential (

) with this new expression.

cancelling

but since h needs to be greater than this height, otherwise it would give a 0 reaction force at point B.

so

I think it's right (had a similar problem at uni).