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?

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