X(1959) (CROSSDIFFERENCE OF PU(23))

 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) = cot2A - cot B cot C
Trilinears           g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = b4 + c4 - a2b2 - a2c2       (M. Iliev, 5/13/07)

Barycentrics    (sin A)f(A,B,C) : (sin B)f(B,C,A) : (sin C)f(C,A,B)

X(1959) lies on these lines:
1,21    2,257    19,326    48,1760    92,304    329,1655    514,661    1444,1761    1762,1812

X(1959) = isogonal conjugate of X(1910)
X(1959) = isotomic conjugate of X(1821)
X(1959) = X(I)-Ceva conjugate of X(J) for these (I,J): (293,1958), (1934,38)
X(1959) = X(I)-cross conjugate of X(J) for these (I,J): (6,2065), (114,2), (230,98), (1692,1976), (1733,1821)
X(1959) = crosspoint of X(1) and X(1581)
X(1959) = crosssum of X(I) and X(J) for these (I,J): (1,1580), (240,1957)

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