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Re:An account of a serious medical emergency on a transocean... by mseebach on Saturday September 03, 2016 @09:09AM (#12419052)
That path is a great circle path, it's simply the shortest path across the face of the earth. It's not a flight plan or anything (but, being the shortest path, it's pretty close to what any given flight would follow).

http://www.gcmap.com/faq/intro#definegc

Also, because it's so far from land, there are special procedures that need to be in place, see eg. ETOPS.

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