X(691) (TRILINEAR POLE OF LINE X(6)X(110))

 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) = a/[(b2 - c2)(2a2 - b2 - c2)]
Barycentrics    g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)

X(691) is the antipode of X(842) on the circumcircle.

X(691) lies on these lines:
3,842    6,843    23,111    30,98    74,511    99,523    110,249    112,250    316,858    376,477    741,923    759,897    805,882

X(691) = reflection of X(I) in X(J) for these (I,J): (23,187), (316,858), (842,3)
X(691) = isogonal conjugate of X(690)
X(691) = cevapoint of X(6) and X(351)
X(691) = X(I)-cross conjugate of X(J) for these (I,J): (23,250), (187,249), (351,6)

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