## X(109) (Ψ(INCENTER, CIRCUMCENTER))

 Interactive Applet

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 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears           a/(cos B - cos C) : b/(cos C - cos A): c/(cos A - cos B)
= g(a,b,c) : g(b,c,a) : g(c,a,b) where g(a,b,c) = a/[(b - c)(b + c - a)]

Barycentrics    a2/(cos B - cos C) : b2/(cos C - cos A): c2/(cos A - cos B)

X(109) = circumcircle-antipode of X(102)
X(109) = Λ(X(1), X(3))
X(109) = trilinear product X(1381)*X(1382)

X(109) lies on these lines:
1,104    2,124    3,102    4,117    7,675    20,151    31,57    34,46    35,73    36,953    40,255    55,103    56,106    58,65    59,901    85,767    98,171    99,643    100,651    101,654    107,162    108,1020    112,163    165,212    191,201    278,917    284,296    478,573    579,608    604,739    649,919    658,927    662,931    840,902

X(109) = midpoint of X(20) and X(151)
X(109) = reflection of X(I) in X(J) for these (I,J): (4,117), (102,3)
X(109) = isogonal conjugate of X(522)
X(109) = anticomplement of X(124)
X(109) = X(I)-Ceva conjugate of X(J) for these (I,J): (59,56), (162,108)
X(109) = cevapoint of X(65) and X(513)
X(109) = X(I)-cross conjugate of X(J) for these (I,J): (56,59), (513,58)
X(109) = crosspoint of X(110) and X(162)
X(109) = crosssum of X(I) and X(J) for these (I,J): (523,656), (652,663)
X(109) = crossdifference of any two points on line X(11)X(1146)
X(109) = X(I)-aleph conjugate of X(J) for these (I,J): (100,1079), (162,580), (651,223)
X(109) = X(I)-beth conjugate of X(J) for these (I,J): (21,104), (59,109), (100,100), (110,109), (765,109), (901,109)
X(109) = trilinear product of X(1381) and X(1382)

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