## X(162) (CEVAPOINT OF X(108) AND X(109))

 Interactive Applet

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 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears           1/(sin 2B - sin 2C) : 1/(sin 2C - sin 2A) : 1/(sin 2A - sin 2B)
= f(a,b,c) : f(b,c,a) : f(c,a,b) , where f(a,b,c) = 1/[(b2 - c2)(b2 + c2 - a2)]

Barycentrics    a/(sin 2B - sin 2C) : b/(sin 2C - sin 2A) : c/(sin 2A - sin 2B)

X(162) lies on these lines:
4,270    6,1013    19,897    27,673    28,88    29,58    31,92    47,158    63,204    100,112    107,109    108,110    190,643    238,415    240,896    242,422    255,1099    412,580    799,811

X(162) = isogonal conjugate of X(656)
X(162) = X(250)-Ceva conjugate of X(270)
X(162) = cevapoint of X(I) and X(J) for this (I,J): (108,109)
X(162) = X(I)-cross conjugate of X(J) for these (I,J): (108,107), (109,110)
X(162) = crosssum of X(810) and X(822)
X(162) = X(I)-aleph conjugate of X(J) for these (I,J): (28,1052), (107,920), (162,1), (648,63)
X(162) = trilinear pole of line X(1)X(19)
X(162) = trilinear product of X(1113) and X(1114)

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