Planet Cutting

Geometry Level 2

On a spherical, land-only planet, there are two cities A and B on the equator.

A railway track--connecting these two cities and going around the planet--can possibly split the planet into two hemispheres, as shown in the diagram.

Given any two cities on this planet, is it always possible to construct an around-the-planet railway track that splits the planet into two hemispheres of equal size?

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 7 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.