Churchmen finally used Circle Line (5)

I believe the answer is:

chord

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'line' is the definition.
(chord is a kind of line)

I can't explain the rest of the clue.

(Other definitions for chord that I've seen before include "Number of notes played together" , "Group of musical notes" , "Combination of notes sounded in harmony" , "line for mathematicians" , "'The Lost - - ' (Sullivan)" .)

I've seen this clue in The Guardian.

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