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# Circum-Medial Triangle

The circum-medial triangle is the circumcevian triangle of a reference triangle with respect to the triangle centroid of (Kimberling 1998, pp. 162-163).

It has trilinear vertex matrix

Its area is

where is the area of .

The following table gives the centers of the circum-medial triangle in terms of the centers of the reference triangle that correspond to Kimberling centers .

 center of circum-medial triangle center of reference triangle circumcenter circumcenter symmedian point trilinear quotient sr(, ) focus of Kiepert parabola sr(, ) isogonal conjugate of isogonal conjugate of isogonal conjugate of odd infinity point first Brocard-axis intercept of circumcircle Steiner point second Brocard-axis intercept of circumcircle Tarry point

Circumcevian Triangle, Medial Triangle

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## References

Kimberling, C. "Triangle Centers and Central Triangles." Congr. Numer. 129, 1-295, 1998.

## Referenced on Wolfram|Alpha

Circum-Medial Triangle

## Cite this as:

Weisstein, Eric W. "Circum-Medial Triangle." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Circum-MedialTriangle.html