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I am trying to figure out whether 3 particular points on Earth's surface are on the same arc (of a great circle) or not. Using Google Earth's (also ArcGIS Earth's) line tool, I see that the points are approximately on the same arc as the one in the middle is only 3 km off where the distance between the neighboring points are more than 1000 km each.

Considering the oblate spheroid shape of Earth, can I confidently conclude from Google (and ArcGIS) Earth measurements that these points are not exactly on the same arc? How probable is it that approximations or some other factors cause 3 km deviation in 1000 km? Is there any method or tool that can help reaching to exact results?

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