This method of constructing the circle is not really correct. Imagine dividing the square horizontally and vertically into 16 pieces. Then the radius is 8. But the 8 points you marked are at a distance sqrt(4^2+7^2)=sqrt(65)>8 from the center, so they are just a tiny bit too far. I guess they could be good guidelines, cause the difference is very tiny, just remember to go sligtly closer to the center.
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