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Mid-Arc Triangle

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 .

 center of mid-arc triangle center of reference triangle circumcenter incenter orthocenter first mid-arc point perspector of abc and orthic-of-orthic triangle third mid-arc point

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.

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