This is a variation on the original task that arose out of the M-B2 movie:
as P moves towards E, Q coincides with E and QP (or EP) becomes a tangent to the circle through C.

The relationship QF = QP becomes EF = EP.

PPS: How does our original GCE O Level task compare to recent GCSE exam questions involving circle theorems? We have a look at this on the next (and final) page: GCSE

a high-res pdf file of this new GEOaa-zz task