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Tixier Point

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TixierPoint

The Tixier point X_(476) is the reflection of the focus of the Kiepert parabola (X_(110)) in the Euler line. It has equivalent trilinear center functions

X_(476)=(csc(B-C))/(1+2cos(2A))
(1)
X_(476)=a/((b^2-c^2)[1+2cos(2A)]).
(2)

It lies on the circumcircle.

The distance between points X_(110) and X_(476) and the Euler line is given by

d=(8Delta|(a^2-b^2)(b^2-c^2)(c^2-a^2)|)/((a^6-a^4b^2-a^2b^4+b^6-a^4c^2+3a^2b^2c^2-b^4c^2-a^2c^4-b^2c^4+c^6)^(3/2)),
(3)

where Delta is the area of the reference triangle.

See also

Kiepert Parabola

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References

Kimberling, C. "Encyclopedia of Triangle Centers: X(476)=Tixier Point." http://faculty.evansville.edu/ck6/encyclopedia/ETC.html#X476.

Referenced on Wolfram|Alpha

Tixier Point

Cite this as:

Weisstein, Eric W. "Tixier Point." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TixierPoint.html

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