## X(42) (CROSSPOINT OF INCENTER AND 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)
= (1 + cos A)(cos B + cos C) : (1 + cos B)(cos C + cos A) : (1 + cos C)(cos A + cos B)
Barycentrics    a2(b + c) : b2(c + a) : c2(a + b)

X(42) lies on these lines:
1,2    3,967    6,31    9,941    25,41    33,393    35,58    37,210    38,518    40,581    48,197    57,1001    65,73    81,100    101,111    165,991    172,199    181,228    244,354    308,313    321,740    517,1064    560,584    649,788    694,893    748,1001    750,940    894,1045    942,1066

X(42) is the {X(1),X(43)}-harmonic conjugate of X(2).

X(42) = reflection of X(321) in X(1215)
X(42) = isogonal conjugate of X(86)
X(42) = isotomic conjugate of X(310)
X(42) = X(I)-Ceva conjugate of X(J) for these (I,J): (1,37), (6,213), (10,71), (55,228)
X(42) = crosspoint of X(I) and X(J) for these (I,J): (1,6), (33,55), (37,65)
X(42) = crosssum of X(I) and X(J) for these (I,J): (1,2), (7,77), (21,81)
X(42) = crossdifference of any two points on line X(239)X(514)
X(42) = X(1)-line conjugate of X(239)
X(42) = X(I)-beth conjugate of X(J) for these (I,J): (21,551), (55,42), (100,226), (210,210), (643,171)

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