Circumradius

The radius of a Triangle's Circumcircle or of a Polyhedron's Circumsphere, denoted . For a Triangle,

(1)

This equation can also be expressed in terms of the Radii of the three mutually tangentCircles centered at the Triangle's Vertices. Relabeling the diagram forthe Soddy Circles with Vertices , , and and the radii , , and, and using

			(2)
			(3)
			(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

For an Archimedean Solid, expressing the circumradius in terms of the Inradius and Midradius gives

			(13)
			(14)

References

Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA: Houghton Mifflin, 1929.

Mackay, J. S. ``Historical Notes on a Geometrical Theorem and its Developments [18th Century].'' Proc. Edinburgh Math. Soc. 5, 62-78, 1886-1887.

• Plücker's Equations
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