NavList:

I wrote previously:
"Suppose you try to find the great circle distance and initial course from anti-Boston to Wellington... How does that distance and course relate to the data that we actually want?"

I couldn't wait. I haven't seen this trick described before, and it's actually rather useful for puzzling out cases that are nearly antipodal. The initial course from A to B is 360° minus the initial course from anti-A to B (a "mirror image" course), and the great circle distance in nautical miles from A to B is just 10800 minus the distance from anti-A to B (10800 is 180·60 --halfway around the spherical globe in nautical miles). 

So suppose I want a great circle track from Dubai in Arabia to Easter Island in the southeast Pacific. Using a common globe and flipping the latitude and longitude, I find that the antipodal point of Dubai isn't far from Pitcairn. From there I can see that I would have to sail ESE roughly 700 nautical miles to reach Easter Island. That means that from Dubai, the great circle distance would be about 10100 miles and the initial course would be WSW. For locations that are within 1500 miles of antipodal, I would say that this is the quickest way to get decent approximate numbers for the distance and initial course on a great circle. Needless to say, in the real world, weather-routing, jet streams, and practical considerations would out-weigh the mathematical niceties of the great circle track. Great circles are far less useful than they appear. And besides, the "real" distance from Dubai to Easter Island is closer to 6875 nautical miles  ...especially after Elon Musk bores a whole straight through the planet.

Frank Reed