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Yff Contact Triangle


YffContactTriangle

The Yff contact triangle DeltaX_AX_BX_C (a term coined here for the first time), is the Cevian triangle of Kimberling center X_(190).

It is the polar triangle of the Yff parabola.

It has the trilinear vertex matrix

 [0 (ac)/(c-a) (ab)/(b-a); (bc)/(b-c) 0 (ab)/(a-b); (bc)/(b-c) (ac)/(c-a) 0].
(1)

The vertices are the points of contact of the Yff parabola with the sidelines of the reference triangle.

Since it is the Cevian triangle of a point on the Steiner circumellipse, it has area

 Delta^'=-2Delta,
(2)

where Delta is the area of the reference triangle and the negative sign indicates that the orientation is reversed.

The circumcircle of the Yff contact triangle is the Yff contact circle.

The triangle centroid of DeltaX_AX_BX_C has triangle center function

 alpha=(b-c)(2a^2+b^2+c^2-2ab-2ac)
(3)

and lies on the lines (2,514), (63,649), (210,513), (514,1022), (612,1027), (661,1211) (P. Moses, pers. comm., Jan. 18, 2005).

Its orthocenter is the Nagel point Na (P. Moses, pers. comm., Jan. 18, 2005).


See also

Yff Contact Circle, First Yff Triangle

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Cite this as:

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

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