The mid-arc triangle is the triangle whose vertices consist of the intersections of
the internal angle bisectors with the incircle ,
where the points of intersection nearest the vertices are chosen (Kimberling 1998,
p. 160).

It has trilinear vertex matrix

where ,
, and .

The incircle is the circumcircle
of the mid-arc triangle.

The following table gives the centers of the mid-arc triangle in terms of the centers of the reference triangle for Kimberling centers
with .

See also Angle Bisector ,

Circumcircle Mid-Arc Triangle ,

Incircle ,

Mid-Arc
Points ,

Tangential Mid-Arc Triangle
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References Kimberling, C. "Triangle Centers and Central Triangles." Congr. Numer. 129 , 1-295, 1998. Referenced on Wolfram|Alpha Mid-Arc Triangle
Cite this as:
Weisstein, Eric W. "Mid-Arc Triangle."
From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/Mid-ArcTriangle.html

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