A triangle
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 .

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 is given by Fewell (2006).

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. London: Macmillian, pp. 251-257,
1893. Referenced on Wolfram|Alpha Circular Triangle
Cite this as:
Weisstein, Eric W. "Circular Triangle."
From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/CircularTriangle.html

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