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Tense performers going over new, touching lines (8)

Ross

I believe the answer is:

tangents

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'touching lines' is the definition.
(I've seen this before)

'tense performers going over new' is the wordplay.
'tense' becomes 't' (abbreviation used in many dictionaries).
'performers going' becomes 'agents' (I can't explain this - if you can you should give a lot more credence to this answer).
'over' is an insertion indicator.
'new' becomes 'n' (common abbreviation eg NT for New Testament).
'agents' placed around 'n' is 'angents'.
't'+'angents'='TANGENTS'

Can you help me to learn more?

(Other definitions for tangents that I've seen before include "Straight lines that touch but don't intersect a curve" , "Touching lines" , "Straight lines that touch curves" , "Straight lines that touche curves" , "Straight lines - ten gnats (anag)" .)

I've seen this clue in The Hindu.
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