## X(479) (X(269)-CROSS CONJUGATE OF X(279))

 Interactive Applet

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This applet was built with the free and multiplatform dynamic geometry software C.a.R..

 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears           (tan A/2 sec A/2)2 : (tan B/2 sec B/2)2 : (tan C/2 sec C/2)2

Barycentrics    tan3(A/2) : tan3(B/2) : tan3(C/2)
= 1/(b + c - a)3 : 1/(c + a - b)3 : 1/(a + b - c)3

Let A' be the point in which the incircle is tangent to a circle that passes through vertices B and C, and define B' and C' cyclically. The lines AA', BB', CC' concur in X(479)

Clark Kimberling and Peter Yff, Problem 10678, American Mathematical Monthly 105 (1998) 666.

X(479) lies on these lines: 7,354    57,279    269,614

X(479) = isogonal conjugate of X(480)
X(479) = X(269)-cross conjugate of X(279)

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