text: Statement a is true.  B is not true, as distinct great circles (which are the lines of spherical geometry) intersect at two points which are antipodes of one another.  C is not true for the reason you observed, as is D.  Thus A is the only statement that can be true.  Of course, we have to understand what a segment is in spherical geometry.  In Euclidean geometry, a line segment is that portion of a line which falls between two points (this is an informal definition, by the way.)  What is true about line segments in Euclidean geometry is that they are paths of minimum distance between their endpoints.  In other words, every other path between two points is longer than the line segment between them.\n\nArmed with this knowledge, lets talk about segments in spherical geometry.  They will be portions of lines (great circles) between two points.  Notice that, given any two points on a sphere, there is at least one great circle that passes through them (if these points are antipodes, there are infinitely many!)  Here's one difference between Euclidean and spherical geometry:  on a sphere, there are two line segments between these points.  Draw a circle and put two points at random on the circle:  you'll see both segments right in front of you.  One of these will be of shorter length that the other (unless you picked antipodal points, in which case the line segments will be of equal length.)  \n\nSo, what does this have to say about shortest distance?  Great circles are what as known as geodesics, which are constructed as paths which minimize distances between points on a space.  Straight lines are the geodesics of Euclidean space.  This isn't trivial to show.  So A is somewhat true, in that it is true that the shortest distance between two points on a sphere is given by a line segment (portion of a great circle.)  It is not true in that any line segment is the shortest distance between those points.