G'day Jim,
If you use Google Earth, there's a function where you can click on a place, say a departure point, and then click on a destination and a great circle, the shortest distance, will be drawn between the two.
The function button is in the top tool bar and looks like a ruler. If you click on KORD and then move over and click on RJAA, Tokyo, you'll find that the line is drawn pretty much right over Winnipeg. Long range air routes generally are very close to the great circle track.
Regards,
BH.