If case 1 is not true then try this:
Are A and B on each other’s anti-meridian?
Anti-meridians are two meridians exactly 180 degrees apart that connect a great circle around the globe.
A: 40N 120E
B: 10N 060W
–> Yes. They are on each other’s anti-=meridian because the longitudes have opposite signs (E and W) and they add up to 180 (120 + 60 = 180).
You can now travel via the north pole or the south pole straight up or down, whichever is shorter.
From 40N to the north pole is 50 degrees.
From 10N to the north pole is 80 degrees.
Total is 130 degrees.
– Great Circle distance = Total degrees x 60 NM = 130 x 60 = 7800 NM
– Track is north until passing the north pole, then it is south.