neat trick, but how do you get it in the EXACT center of the new document?You can also do it like this:
New document - 300dpi
3400x3400 pixels (3300x3300 pixels is 11" and it's nice to have some edge room in PS I think but you can do it however you like)
go to the Elliptical Marquee tool and in the menu bar for style use "fixed size" and enter the amount (3300/3300)
it will select a circle in that precise size.
I screenshot it (and added a white fill so you could see it better)