What type of circle does not intersect the center point of the Earth?

The correct choice is the small circle because a small circle is defined as any circle on the surface of a sphere that does not have the same center as the sphere and does not pass through the sphere's center. In the context of the Earth, which is roughly spherical, small circles are created by lines of latitude that are not the equator. For example, the Arctic Circle and the Tropic of Cancer are small circles; they do not intersect the Earth's center.

In contrast, great circles are those that do intersect the center of the Earth, including the equator and all lines of longitude. Great circles represent the largest possible circle that can be drawn on the surface of a sphere, effectively dividing the sphere into two equal hemispheres.

Longitude and latitude lines themselves are not types of circles, but rather a coordinate system used for navigation and mapping. Lines of latitude at the equator are great circles, while those further north or south are classified as small circles. Thus, the distinction lies in the relationship to the center of the Earth, where the small circles do not intersect it.