great circle

noun
1.
a circle on a spherical surface such that the plane containing the circle passes through the center of the sphere. Compare small circle.
2.
a circle of which a segment represents the shortest distance between two points on the surface of the earth.

Origin:
1585–95

Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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Collins
World English Dictionary
great circle
 
n
Compare small circle a circular section of a sphere that has a radius equal to that of the sphere

Collins English Dictionary - Complete & Unabridged 10th Edition
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Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009
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American Heritage
Science Dictionary
great circle  
A circle on the surface of a sphere whose plane passes through the center of the sphere. The Earth's equator is a great circle on the sphere of the globe.
The American Heritage® Science Dictionary
Copyright © 2002. Published by Houghton Mifflin. All rights reserved.
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Example sentences
We had a few hours between trains and were taken by a guide for a walk eastward
  in a great circle.
Everyone recognizes that in the great circle of life, some individuals have to
  lose so that others can survive.
Not only does it find distances, it draws great circle routes between points.
Any straight line drawn on the map is on a great circle, but directions are
  true only from center point of projection.
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