Fitting hexagons in a circle


I've got a problem,
I'm trying to design a code to make hexagons fit inside of a circle.
Heres how my problem looks like:
The hexagons have a set size, say a radius of one.
Now I would like to calculate how many, and wich of these hexagons fit in a circle of a certain radius placed on a grid of hexagons. The circle always has a hexagon exactly in the center of it.
Is there some clever way to do this without checking for every hexagon if it inside or outside of the circle?
Your help would be appreciated!
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