Crossword Genius

Safe crossing two New England states' border (9)

Ross

I believe the answer is:

perimeter

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'border' is the definition.
('perimeter' can be a synonym of 'border')

'safe crossing two new england states'' is the wordplay.
'safe' becomes 'peter' (I've seen this before).
'crossing' is an insertion indicator.
'two new england states'' becomes 'rime' (I can't explain this - if you can you should believe this answer much more).
'peter' placed around 'rime' is 'PERIMETER'.

Can you help me to learn more?

(Other definitions for perimeter that I've seen before include "Prime tree (anag.)" , "limits" , "Exterior of a plane figure" , "Continuous boundary" , "Outer boundary" .)

I've seen this clue in The Telegraph.
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