A triangle arcs . By extending the arcs into
complete circles, the points of intersection associated
triangles to
The circular triangle and its associated circles have a total of eight incircles and six circumcircles . These systems of circles
have some remarkable properties, including the Hart circle ,
which is an analog of the nine-point circle
in Feuerbach's theorem .
A closed-form set of formulas for the area of circular triangles like
See also Apollonius' Problem ,
Arc ,
Associated Triangles ,
Circle-Circle
Intersection ,
Feuerbach's Theorem ,
Hart
Circle ,
Haruki's Theorem ,
Johnson's
Theorem ,
Nine-Point Circle ,
Spherical
Triangle
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References Fewell, M. "Area of Common Overlap of Three Circles." Australian Dept. Defense. Oct. 2006. http://www.dsto.defence.gov.au/publications/4815/DSTO-TN-0722.pdf . Lachlan,
R. "Properties of a Circular Triangle." §397-404 in An
Elementary Treatise on Modern Pure Geometry. Referenced on Wolfram|Alpha Circular Triangle
Cite this as:
Weisstein, Eric W. "Circular Triangle."
From MathWorld https://mathworld.wolfram.com/CircularTriangle.html
Subject classifications
formed by three circular arcs. By extending the arcs into
complete circles, the points of intersection 
, 
, and 
are obtained. This gives the three circular triangles, 
, 
, 
, and 
, which are called the associated
triangles to 
.
is given by Fewell (2006).
