Editing Spherical circle (section)

=== Extrinsic characterization ===
[[Image:Esfera-raio-circulomenor.png|right|thumb|<math>BC^2=AB^2+AC^2</math>, where ''C'' is the center of the sphere, ''A'' is the center of the small circle, and ''B'' is a point in the boundary of the small circle. Therefore, knowing the radius of the sphere, and the distance from the plane of the small circle to C, the radius of the small circle can be determined using the Pythagorean theorem.]]

If the sphere is [[Isometry|isometrically]] [[embedding|embedded]] in [[Euclidean space]], the sphere's [[intersection (geometry)|intersection]] with a [[plane (geometry)|plane]] is a circle, which can be interpreted extrinsically to the sphere as a Euclidean circle: a locus of points in the plane at a constant [[Euclidean distance]] (the ''extrinsic radius'') from a point in the plane (the ''extrinsic center''). A great circle lies on a plane passing through the center of the sphere, so its extrinsic radius is equal to the radius of the sphere itself, and its extrinsic center is the sphere's center. A small circle lies on a plane ''not'' passing through the sphere's center, so its extrinsic radius is smaller than that of the sphere and its extrinsic center is an arbitrary point in the interior of the sphere. Parallel planes cut the sphere into parallel (concentric) small circles; the pair of parallel planes tangent to the sphere are tangent at the poles of these circles, and the [[diameter]] through these poles, passing through the sphere's center and perpendicular to the parallel planes, is called the ''axis'' of the parallel circles.

The sphere's intersection with a second sphere is also a circle, and the sphere's intersection with a concentric [[right circular cylinder]] or [[right circular cone]] is a pair of antipodal circles.