G'day Standby,
If you use google earth, start a ruler at Auckland and finish it at Santiago. This will give you the great circle track between the two cities, then overlay the Lat/Long grid on top and you'll find the farthest south you get is S52.5 deg. At 60nm/degree of lat and being 37.5 degrees from the pole gives you 37.5 x 60 = 2250nm distance from the pole.
Regards,
BH