## X(258) (CONGRUENT INCIRCLES ISOSCELIZER POINT)

 Interactive Applet

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 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears           f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = 1/(cos B/2 + cos C/2 - cos A/2)
= g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = 1 + sin(B/2) + sin(C/2) - sin(A/2)
Trilinears           tan(A/2) - sec(A/2) : tan(B/2) - sec(B/2) : tan(C/2) - sec(C/2)      (M. Iliev, 4/12/07)

Barycentrics    (sin A)f(A,B,C) : (sin B)f(B,C,A) : (sin C)f(C,A,B)

In Yff's isoscelizer configuration, if X = X(258), then the isosceles triangles Ta, Tb, Tc have congruent incircles.

X(258) lies on these lines: 1,164    57,173    259,289

X(258) = isogonal conjugate of X(173)
X(258) = X(259)-cross conjugate of X(1)
X(258) = X(366)-aleph conjugate of X(363)

This is a joint work of
Humberto José Bortolossi, Lis Ingrid Roque Lopes Custódio and Suely Machado Meireles Dias.