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Here's the circle:

Circle

I've always been extruding and then scaling the circle inwards. But when I then make a face, there's an ngon. It's not very noticeable, so I've been sticking to that method all the time. But now I am wondering if there's a method that involves only quads. Would that even be possible?

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there must be several ways to do it, like the following ones, I'm not sure how it could be useful though. As said by Robin, an easy way to begin is to ctrl F > Grid Fill, then modify the grid that has been created with some alt shift S to make your selection round:

enter image description here

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One handy thing to know is that, given an empty circle with an even number of edges, Ctrl F > Grid Fill will choose the right number of spans, and do the right thing to generate this pattern:

enter image description here

If you suspect you will want to retain an edge-loop around the outside for convenient beveling. extruding, and so on, it may be better to inset the circle first, just filling the center hole this way.

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