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 
and circumradius 
of a triangle are connected by
where 
is the distance between the incenter and circumcenter
(Coolidge 1971, p. 45).
See also
Bicentric Polygon,
Bicentric
Quadrilateral,
Euler Triangle Formula
Explore with Wolfram|Alpha
References
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. https://mathworld.wolfram.com/BicentricTriangle.html
Subject classifications
