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Ceva Conjugate


CevaConjugate

Let P=alpha_1:beta_1:gamma_1 and Q=alpha_2:beta_2:gamma_2 be points, neither of which lie on a sideline of the reference triangle DeltaABC. The P-Ceva conjugate X of Q is then given by the perspector of the Cevian triangle of P and the anticevian triangle of Q. It has trilinear coordinates

 alpha_2(-(alpha_2)/(alpha_1)+(beta_2)/(beta_1)+(gamma_2)/(gamma_1)):beta_2(-(beta_2)/(beta_1)+(gamma_2)/(gamma_1)+(alpha_2)/(alpha_1)) 
 :gamma_2(-(gamma_2)/(gamma_1)+(alpha_2)/(alpha_1)+(beta_2)/(beta_1))

(Kimberling 1998, p. 57).


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References

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

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Ceva Conjugate

Cite this as:

Weisstein, Eric W. "Ceva Conjugate." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CevaConjugate.html

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