Great Circle Definition and Properties

A great circle is the largest possible circle that can be drawn on the surface of a sphere. It is formed when a plane passes through the center of the sphere. Every great circle divides the sphere into two equal hemispheres.

Evaluating Statements about Great Circles

• Statement 1: 'Every great circle divides the Earth into equal halves.' This statement is correct. By definition, a great circle splits the sphere into two identical hemispheres.
• Statement 2: 'Every great circle is a circumference of the Earth.' This statement is correct. The perimeter of any great circle drawn on the Earth's surface is equivalent to the Earth's circumference.
• Statement 4: 'Great circle is the largest circle that can be drawn around the Earth through two particular points.' This statement is correct. For any two points on a sphere (not antipodal), the unique great circle passing through them represents the largest possible circular path on the sphere's surface.
• Statement 3: 'Great circles mark the longest travel routes between locations on the Earth's surface.' This statement is incorrect. Great circle routes are known to be the shortest possible paths between two points on a sphere's surface. Airlines and ships often use these routes to minimize travel distance and time.

Conclusion: The Incorrect Statement

The statement that is not correct is that great circles mark the longest travel routes. In reality, they represent the shortest possible routes.