## X(75) (ISOTOMIC CONJUGATE OF INCENTER)

 Interactive Applet

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 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears           1/a2 : 1/b2 : 1/c2
= 1/(1 - cos 2A) : 1/(1 - cos 2B) : 1/(1 - cos 2C)

Barycentrics    1/a : 1/b : 1/c

This is the center X(37) of the anticomplementary triangle.

X(75) lies on these lines:
1,86    2,37    6,239    7,8    9,190    10,76    19,27    21,272    31,82    32,746    38,310    43,872    48,336    77,664    99,261    100,675    101,767    141,334    144,391    158,240    194,1107    225,264    234,556    257,698    280,309    299,554    523,876    537,668    689,745    700,971    753,789    758,994    799,897    811,1099

X(75) is the {X(7),X(8)}-harmonic conjugate of X(69).

X(75) = reflection of X(I) in X(J) for these (I,J): (192,37), (335,1086), (984,10)
X(75) = isogonal conjugate of X(31)
X(75) = isotomic conjugate of X(1)
X(75) = complement of X(192)
X(75) = anticomplement of X(37)
X(75) = X(I)-Ceva conjugate of X(J) for these (I,J): (76,312), (274,2), (310,76), (314,69)
X(75) = cevapoint of X(I) and X(J) for these (I,J): (1,63), (2,8), (7,347), (10,321), (244,514)

X(75) = X(I)-cross conjugate of X(J) for these (I,J):
(1,92), (2,85), (7,309), (8,312), (10,2), (38,1), (63,304), (244,514), (307,69), (321,76), (347,322), (522,190)

X(75) = crosspoint of X(I) and X(J) for these (I,J): (2,330), (274,310)
X(75) = crossdifference of any two points on line X(667)X(788)
X(75) = X(I)-Hirst inverse of X(J) for these (I,J): (2,350), (334,335)
X(75) = X(83)-aleph conjugate of X(31)

X(75) = X(I)-beth conjugate of X(J) for these (I,J):
(8,984), (75,7), (99,77), (314,75), (522,876), (645,9), (646,75), (668,75), (811,342)

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