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# Yff Central Triangle

Let three isoscelizers , , and be constructed on a triangle , one for each side. This makes all of the inner triangles similar to each other. However, there is a unique set of three isoscelizers for which the four interior triangles , , , and are congruent. The innermost triangle is called the Yff central triangle (Kimberling 1998, pp. 94-95).

It has trilinear vertex matrix

where , , and (Kimberling 1998, p. 172; typo corrected).

The original triangle is the extangents triangle of the Yff central triangle .

The circumcircle of the Yff central circle is the Yff central circle.

The following table gives the centers of the Yff central triangle in terms of the centers of the reference triangle for Kimberling centers with .

 center of Yff central triangle center of reference triangle Clawson point congruent isoscelizers point Bevan point incenter internal similitude center of circumcircle and incircle Yff center of congruence orthocenter of the contact triangle first mid-arc point

Extangents Triangle, Isoscelizer, Yff Center of Congruence, Yff Central Circle

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## References

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

## Referenced on Wolfram|Alpha

Yff Central Triangle

## Cite this as:

Weisstein, Eric W. "Yff Central Triangle." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/YffCentralTriangle.html