In article .com,
Peter Vos writes
I saw a post saying the KX stop is the only stop on the Circle Line
where trains in both directions are separated by an central island
platform.

This is wrong. Gloucester Road and South Kensington also meet this
description. In addition, Edgware Road and Aldgate have two island
platforms and Circle line trains use the outermost faces (usually but
not required at the former, required at the latter).

Outer Rail trains also have platforms on the right at Tower Hill and
Mansion House.

The question I have is how far would you have to travel in either
direction from KX before the doors that open at KX would be used again?

Edgware Road (see above) and Aldgate.

Would you get as far as Edgware and Liverpool?

No. Circle Line trains don't go to either.

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