spherical geometry, help asap! :)?

Question

describe all the ways in which two distinct great cricles can intersect on the sphere. can two great circles ever be parallel?

if i great circle is on a sphere, what figure can be drawn that is always the same distance from the great circle, can it be a great circle?

Answer 1

Two distinct great circles intersect at two points which are opposite sides of the sphere. Whether or not great circles can be parallel depends on what you mean by parallel.

For a great circle on a sphere you can draw another circle on the sphere so that every point in the second circle has the same distance from the great circle, but this second circle will not be great, only mediocre :-)

Answer 2

Two distinct great circles intersect in two points on the sphere which are endpoints of a diameter of the sphere.

One definition of a great circle of a sphere is the intersection of the sphere with a plane that passes through the center of the sphere. If two planes have a point in common, they cannot be parallel. Therefore, two distinct great circles cannot be parallel.

If a figure is always the same distance from a great circle, it must lie in a plane that is parallel to the plane that defines the great circle. Hence, any such figure is a circle (or part of such a circle) that is the intersection of the sphere with a plane parallel to the great circle's plane. These circles are sometimes called "small circles". Lines of latitude other than the equator (which is a great circle) are small circles. Since two distinct great circles always intersect, but are not coincident, they cannot be always the same distance from each other.

Answer 3

Sorry I don't have an answer, but i think you're doing the same project as me. My questions are worded the exact same way yours are. do you think you could help me out a little?