## X(79) (ISOGONAL CONJUGATE OF X(35))

 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           1/(1 + 2 cos A) : 1/(1 + 2 cos B) : 1/(1 + 2 cos C)
= f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = bc/(b2 + c2 - a2 + bc)
= g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = (sin A/2)(sin 3B/2)(sin 3C/2)

Barycentrics    h(a,b,c) : h(b,c,a) : h(c,a,b), where h(a,b,c) = 1/(b2 + c2 - a2 + bc)

Let A' be the reflection of X(1) in sideline BC, and define B' and C' cyclically. Then the lines AA', BB', CC' concur in X(79). (Eric Danneels, Hyacinthos 7892, 9/13/03)

X(79) lies on these lines:
1,30    8,758    9,46    12,484    21,36    33,1063    34,1061    35,226    57,90    65,80    104,946    314,320    388,1000

X(79) = reflection of X(191) in X(442)
X(79) = isogonal conjugate of X(35)
X(79) = isotomic conjugate of X(319)
X(79) = cevapoint of X(481) and X(482)
X(79) = crosssum of X(55) and X(1030)

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