Bitter centre displayed by each side (4)

I believe the answer is:

acid

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'bitter' is the definition.
(acid can mean bitter-tasting)

'centre displayed by each side' is the wordplay.
'centre' indicates the central letters.
'displayed' becomes 'sat' (sitting is a kind of displaying).
'by' says to put letters next to each other.
'each side' becomes 'cid' (I am not sure about this - if you are sure you should believe this answer much more).
The middle of 'sat' is 'a'.
'a'+'cid'='ACID'

Can you help me to learn more?

(Other definitions for acid that I've seen before include "- - -drop, sweet" , "Polluted precipitation" , "Substance with pH of less than 7" , "Cutting" , "Sour - vitriolic" .)

I've seen this clue in The Irish Times.

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