## X(598) (ISOGONAL CONJUGATE OF X(574))

 Interactive Applet

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 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears            bc/(a2 - 2b2 - 2c2) : ca/(b2 - 2c2 - 2a2) : ab/(c2 - 2a2 - 2b2)
Barycentrics    1/(a2 - 2b2 - 2c2) : 1/(b2 - 2c2 - 2a2) : 1/(c2 - 2a2 - 2b2)

The Lemoine ellipse is the ellipse inscribed in triangle ABC having X(2) and X(6) as foci. Let A' be where this ellipse meets sideline BC, and define B' and C' cyclically. Then triangles ABC and A'B'C' are perspective, and their perspector is X(598). (Bernard Gibert, 1/5/01, Hyacinthos #2334)

X(598) lies on these lines: 2,187    4,575    6,671    30,262    76,524    98,381

X(598) = isogonal conjugate of X(574)
X(598) = isotomic conjugate of X(599)

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