We are asked whether figure W is a line in spherical geometry. We model the given picture by the following sphere.
A line in spherical geometry — or geometry on a sphere — is a great circle. A great circle (also known as an orthodrome) of a sphere can be defined in few ways.
It is one of the largest circles that can be drawn on a sphere.
It is the intersection of the sphere and a plane that passes through the center of the sphere.
It is a circle that passes through poles of the sphere. The poles are the pair of antipodal points — the points on the sphere that are the endpoints of a diameter of the sphere.
Note that W is a circle, but it is not the largest circle that we can draw on the sphere.
Note that O is bigger than W. This tells us that W is not a great circle. Therefore, it is not a line in spherical geometry.
