## X(107) (Ψ(SYMMEDIAN POINT, ORTHOCENTER))

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

Barycentrics    1/[(b2 - c2)(b2 + c2 - a2)2] : 1/[(c2 - a2)(c2 + a2 - b2)2] : 1/[(a2 - b2)(a2 + b2 - c2)2]

X(107) = Ψ(X(6), X(4))

X(107) lies on these lines:
2,122    4,74    24,1093    25,98    27,103    28,104    29,102    51,275    100,823    109,162    110,648    111,393    158,759    186,477    250,687    450,511    468,842    741,1096

X(107) = reflection of X(I) in X(J) for these (I,J): (4,133), (1294,3)
X(107) = isogonal conjugate of X(520)
X(107) = anticomplement of X(122)
X(107) = cevapoint of X(4) and X(523)
X(107) = X(I)-cross conjugate of X(J) for these (I,J): (24,250), (108,162), (523,4)
X(107) = trilinear pole of line X(4)X(6)

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