Cycling around African country’s capital city (4)

I believe the answer is:

lima

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'capital city' is the definition.
(capital of Peru)

'cycling around african country's' is the wordplay.
'around' means to look at the middle letters.
'african country's' becomes 'ima' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
The central letter of 'cycling' is 'l'.
'l'+'ima'='LIMA'

Can you help me to learn more?

(Other definitions for lima that I've seen before include "distant city" , "Mail to Peru's capital" , "Mail to capital of Peru" , "city (like 22)" , "South American capital" .)

I've seen this clue in The Times.

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