Crossword Genius

In the centre of the motorway at the end of the road (3)

Ross

I believe the answer is:

mid

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'in the centre of' is the definition.
I can't tell whether this definition defines the answer.

'motorway at the end of the road' is the wordplay.
'motorway' becomes 'MI' (resembles M1, English motorway).
'at the end of' suggests the final letters.
The final letter of 'road' is 'd'.
'mi'+'d'='MID'

'the' acts as a link.

Can you help me to learn more?

(Other definitions for mid that I've seen before include "Of the central part" , "Prefix meaning centre" , "Dim sort of prefix" , "Denote the centre point" .)

I've seen this clue in the Evening Standard.
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