## X(219) (X(8)-CEVA CONJUGATE OF X(55))

 Interactive Applet

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 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears           cos A cot A/2 : cos B cot B/2 : cos C cot C/2
= (sin A)/(1 - sec A) : (sin B)/(1 - sec B) : (sin C)/(1 - sec C)
= 1/(csc A - 2 csc 2A) : 1/(csc B - 2 csc 2B) : 1/(csc C - 2 csc 2C)
= a(b + c - a)(b2 + c2 - a2) : b(c + a - b)(c2 + a2 - b2) : c(a + b - c)(a2 + b2 - c2)

Barycentrics    sin 2A cot A/2 : sin 2B cot B/2 : sin 2C cot C/2

X(219) lies on these lines:
1,6    3,48    8,29    10,965    19,517    40,610    41,1036    55,284    56,579    63,77    101,102    144,347    200,282    206,692    255,268    278,329    332,345    346,644    572,947    577,906    604,672

X(219) = isogonal conjugate of X(278)
X(219) = isotomic conjugate of X(331)
X(219) = X(I)-Ceva conjugate of X(J) for these (I,J): (8,55), (63,3), (283,212)
X(219) = X(I)-cross conjugate of X(J) for these (I,J): (48,268), (71,9), (212,3)
X(219) = crosspoint of X(I) and X(J) for these (I,J): (8,345), (64,78)
X(219) = crosssum of X(I) and X(J) for these (I,J): (19,34), (56,608)
X(219) = X(I)-beth conjugate of X(J) for these (I,J): (101,478), (219,48), (644,219)

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