## X(102) (Λ(INCENTER, ORTHOCENTER))

 Interactive Applet

You can move the points A, B and C (click on the point and drag it).
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You can also construct all centers related with this one (as described in ETC) using the “Run Macro Tool”. To do this, click on the icon , select the center name from the list and, then, click on the vertices A, B and C successively.

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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           f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = 1/[sin B (sec A - sec B) + sin C (sec A - sec C)]
= g(a,b,c) : g(b,c,a) : g(c,a,b), where
g(a,b,c) = a/[2a5 + (b + c)a4 - 2(b2 + c2)a3 - (b + c)(b2 - c2)2]

Barycentrics    g(A,B,C) : g(B,C,A) : g(C,A,B), where
g(A,B,C) = (sin A)/[sin B (sec A - sec B) + sin C (sec A - sec C)]

X(102) = circumcircle-antipode of X(109)
X(102) = Λ(X(1), X(4))

X(102) lies on these lines:
1,108    2,117    3,109    4,124    19,282    29,107    40,78    73,947    77,934    99,332    101,198    103,928    110,283    112,284    226,1065    516,929

X(102) = midpoint of X(20) and X(153)
X(102) = reflection of X(I) in X(J) for these (I,J): (4,124), (109,3), (151,117)
X(102) = isogonal conjugate of X(515)
X(102) = complement of X(151)
X(102) = anticomplement of X(117)
X(102) = X(21)-beth conjugate of X(108)

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