Re:An account of a serious medical emergency on a transocean...
by mseebach on Saturday September 03, 2016 @09:53AM
(#12419185)
That map does not show true flight paths, those are heavily stylised.
This is a true flight path, and it's much closer to the great circle: https://www.flightradar24.com/DAL200/ae190b1
You can use this website to see the true flight path for the Johannessburg flight: http://dl.fltmaps.com/en [enter Atlanta and Johannesburg as the endpoints]
EDIT: Can't find an FAA source about distances to airport, but here's a related Wikipedia page. https://en.wikipedia.org/wiki/ETOPS