Great Circle
A great circle is the largest possible circle that can be drawn on the surface of a sphere. Its center coincides with the center of the sphere, dividing the sphere into two equal hemispheres. In Earth geometry, all lines of longitude and the equator are great circles.
Example
The shortest distance between two points on the surface of the Earth lies along the arc of a great circle connecting them. The distance $d$ along a great circle is given by $d = \frac{\theta}{360^\circ} \times 2\pi R$, where $\theta$ is the angle subtended at the center of the Earth and $R$ is the Earth's radius.