Great Circles and Spherical Geometry

What is a great circle?

• A circle with the largest radius on Earth

• The intersection of a sphere's surface and a plane passing through its center

• A circle that does not pass through the center of the sphere

• Any circular path on the surface of the Earth

What is the shortest surface distance between two points on a sphere?

• Along a rhumb line

• Along a great circle

• Along a latitude line

• Along the equator

How many great circles connect two points on a sphere that are not antipodal?

• Infinitely many

• Exactly one

• Two

• Zero

What happens at the vertices of a great circle?

• The great circle crosses the equator

• The direction of the circle is due east or west

• The circle bisects the sphere

• The circle intersects with rhumb lines

What is the relationship between points 180° apart on a great circle?

• They have the same latitude with opposite names

• They are connected by a rhumb line

• They are the vertices of a spherical triangle

• They always lie on the equator

On a Mercator projection, how does a great circle appear?

• As a straight line

• As a sine curve concave to the equator

• As a circular arc

• As a parabola

What is a rhumb line in relation to a great circle?

• A line that forms the shortest path between two points

• A straight line that intersects the great circle at the poles

• A chord of the great circle's curve on a Mercator projection

• A circular arc passing through the sphere's center

What determines the usability of a great circle route for navigation?

• Its intersection with rhumb lines

• The absence of land and dangerous waters

• The curvature of the route relative to the equator

• Its appearance on Mercator charts

What is a spherical triangle?

• A triangle formed by three latitude lines

• A triangle formed by three arcs of great circles

• A triangle that lies entirely on the equator

• A triangle that contains angles summing to 180°

What are the vertices of a spherical triangle?

• The intersection points of the bounding arcs

• The points of greatest latitude on a great circle

• The endpoints of a rhumb line

• The points where arcs intersect the equator