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Cut a sphere with a plane and you get a circle. If the plane goes through the centre of
the sphere then you get the largest possible circle, and that's called a Great Circle.
The Equator is a Great Circle of the Earth, as is any line of Longitude.
The Great Circle gives the line of shortest distance between two points on a sphere however using Great Circles to navigate over the surface of the Earth is impractical as, in most routes, the compass bearing is continuous changing throughout the journey. (see Bearings)
In practical navigation, the Great Circle routes are broken into a chain of shorter Rhumb lines between points on the Great Circle.
Because of the Earth's irregular shape, not all Great Circles are the same size.
See also: Units of Distance