What is the term for a plane that passes through the Earth intersecting the center point?

The term for a plane that passes through the Earth intersecting the center point is a Great Circle. A Great Circle represents the largest possible circle that can be drawn on a sphere, effectively dividing it into two equal halves. The Equator is a classic example of a Great Circle, as are the meridians of longitude which, when extended, always intersect at the poles.

In contrast, a Small Circle is any circle that does not divide the sphere into two equal halves, such as the circles of latitude (other than the Equator). Latitude lines indicate how far north or south a location is from the Equator, but they do not represent Great Circles except for the Equator itself. Longitude is a measure of distance east or west of the Prime Meridian but refers to the lines converging at the poles, not to a plane that intersects the Earth's center. Thus, the definition and properties of a Great Circle make it the correct answer.