## X(101) (Ψ(INCENTER, SYMMEDIAN POINT))

 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           a/(b - c) : b/(c - a) : c/(a - b)
= a(a - b)(a - c) : b(b - c)(b - a) : c(c - a)(c - b)

Barycentrics    a2/(b - c) : b2/(c - a) : c2/(a - b)

X(101) = circumcircle-antipode of X(103)
X(101) = Ψ(X(1), X(6))

X(101) lies on these lines:
1,41    2,116    3,103    4,118    6,106    9,48    10,98    19,913    20,152    31,609    32,595    36,672    37,284    40,972    42,111    56,218    58,172    59,657    71,74    75,767    78,205    99,190    100,644    102,198    109,654    110,163    514,664    517,910    522,929    560,713    643,931    649,901    651,934    663,919    667,813    668,789    692,926    733,904    743,869    761,984    765,898

X(101) = midpoint of X(20) and X(152)
X(101) = reflection of X(I) in X(J) for these (I,J): (4,118), (103,3), (150,116)
X(101) = isogonal conjugate of X(514)
X(101) = complement of X(150)
X(101) = anticomplement of X(116)
X(101) = X(59)-Ceva conjugate of X(55)
X(101) = cevapoint of X(354) and X(513)
X(101) = X(I)-cross conjugate of X(J) for these (I,J): (55,59), (199,250)
X(101) = crosssum of X(I) and X(J) for these (I,J): (513,650), (523,661), (649,1459)
X(101) = crossdifference of any two points on line X(11)X(244)
X(101) = X(I)-aleph conjugate of X(J) for these (I,J): (100,165), (509,1052), (662,572), (664,169)
X(101) = X(I)-beth conjugate of X(J) for these (I,J): (21,105), (644,644)

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