Hope this helps
The basic problem is that the chart projections are inherently non-linear, so an 800 nm circle for example would not be a consistent size across the chart and would actually have a slight egg shape depending on where you were relative to the projection point.
I took a look at some of my pacific examples, and you can definitely see a difference particularly on those which cover a large area. How much difference and how close is close enough? I am not a cartographer so can't really comment on that, however suffice to say there is some degree of inaccuracy when using this approach