How clustered index stored on disk ?

It was interview. I had a question - how clustered index stored.

I answered - it is a binnary tree stored physically on the disk.

If we have clustered index then rows will be sorted ascending by it value.

If it hasn't clustered index the physical order will mesh.

Then they asked. So for example what happened if we added record in the middle of the tree ? Do you mean that all record below inserted record physically moved on other place ?

I understood that of course no, but can't explain how binary tree is stored on the disk .

So the main question - what happened on this disk when your insert new record for table who has clustered index ?

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