Bicentric Triangle

All triangles are bicentric, i.e., possess both an incircle and a circumcircle. This is not necessarily the case for polygons with four or more sides.

The inradius r and circumradius R of a triangle are connected by


where d is the distance between the incenter and circumcenter (Coolidge 1971, p. 45).

See also

Bicentric Polygon, Bicentric Quadrilateral, Euler Triangle Formula

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Coolidge, J. L. A Treatise on the Geometry of the Circle and Sphere. New York: Chelsea, 1971.van Lamoen, F. M. "Bicentric Triangles." Nieuw Arch. Wisk. 17, 363-372, 1999.

Referenced on Wolfram|Alpha

Bicentric Triangle

Cite this as:

Weisstein, Eric W. "Bicentric Triangle." From MathWorld--A Wolfram Web Resource.

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