Circumference as measured by fairy instrument? (9)

I believe the answer is:

perimeter

I'm a little stuck... Click here to teach me more about this clue!

'circumference' is the definition.
(I know that circumference can be written as perimeter)

'by fairy instrument?' is the wordplay.
'by' is a charade indicator (letters next to each other).
'fairy' becomes 'peri' (Persian mythological being).
'instrument?' becomes 'meter' (meter is a kind of instrument).
'peri'+'meter' is 'PERIMETER'.

'as measured' is the link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.

Can you help me to learn more?

(Other definitions for perimeter that I've seen before include "Continuous boundary" , "limits" , "Prime tree (anag.)" , "Border" , "edge" .)

I've seen this clue in The Irish News.

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