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I understand that at which point is completely grammatical and I know how and when to use it, but it just now struck me as an odd phrase.

What exactly is which doing here? How does it make the phrase make sense?

Example:
I ran ten miles without stopping, at which point I felt sick.

I want to think which is being used in the usual sense referring to a selection (e.g., which of these), but I'm not quite sure.

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  • "at which point" identifies a point (that is, selects the point).
    – phoog
    Commented Sep 30, 2015 at 9:12
  • @phoog That doesn't tell me much apart from knowing what each word means.
    – Adam
    Commented Sep 30, 2015 at 15:03
  • I'd say it's being used as a determiner. See example sentences here.
    – Tragicomic
    Commented Oct 1, 2015 at 2:48

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Which is here used as a determiner :

  • (followed by a noun): Which colour do you like best?

  • used when someone knows, says, is not certain about etc the specific choice between two or more possibilities.

    • They’re all so pretty – I don’t know which one to choose.
    • It was either whisky or vodka – I forget which.
    • Did he say which hotel he was staying at?
    • I don’t know which is worse – spending Christmas alone or watching my friends get drunk.

(macmillandictionary.com)

  • At which point, that is, the point at which; which here identifies/determines a specific point, among other possible points, at which the action in question is referred to.
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  • A relative determiner, I might add.
    – AJK432
    Commented Apr 30, 2019 at 14:54

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