In the
Euclidean plane, two circles that are concentric necessarily have different radii from each other. However, circles in three-dimensional space may be concentric, and have the same radius as each other, but nevertheless be different circles. For example, two different
meridians of a terrestrial
globe are concentric with each other and with the
globe of the earth (approximated as a sphere). More generally, every two
great circles on a sphere are concentric with each other and with the sphere. By
Euler's theorem in geometry on the distance between the
circumcenter and
incenter of a triangle, two concentric circles (with that distance being zero) are the
circumcircle and
incircle of a triangle
if and only if the radius of one is twice the radius of the other, in which case the triangle is
equilateral. The circumcircle and the incircle of a
regular n-gon, and the regular
n-gon itself, are concentric. For the circumradius-to-inradius ratio for various
n, see Bicentric polygon#Regular polygons. The same can be said of a
regular polyhedron's
insphere,
midsphere and
circumsphere. The region of the plane between two concentric circles is an
annulus, and analogously the region of space between two concentric spheres is a
spherical shell. For a given point
c in the plane, the set of all circles having
c as their center forms a
pencil of circles. Each two circles in the pencil are concentric, and have different radii. Every point in the plane, except for the shared center, belongs to exactly one of the circles in the pencil. Every two disjoint circles, and every hyperbolic pencil of circles, may be transformed into a set of concentric circles by a
Möbius transformation. == Applications and examples ==