Take courses at home in centre of Philadelphia (4)

I believe the answer is:

dine

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'take courses at home in centre of philadelphia' is the definition.
I can't tell whether this defines the answer.

'home in centre of philadelphia' is the wordplay.
'home' becomes 'in' ('he's home' can mean 'he's in').
'in' means one lot of letters goes inside another.
'centre of' indicates the central letters.
The central letters of 'philadelphia' are 'de'.
'in' inserted into 'de' is 'DINE'.

Can you help me to learn more?

(Other definitions for dine that I've seen before include "Have supper" , "Eat with Enid?" , "Take meal" , "Eat main meal" , "Take dinner" .)

I've seen this clue in The Times.

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