## X(491) (CEVAPOINT OF X(2) AND X(487))

 Interactive Applet

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 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) = (cos A)(1 - csc A sin B sin C) + cos B cos C
Trilinears            sin(A - π/4)csc2A : sin(B - π/4)csc2B : sin(C - π/4)csc2C      (M. Iliev, 4/12/07)
Trilinears            (1 - cot A) csc A : (1 - cot B) csc B : (1 - cot C) csc C      (M. Iliev, 4/12/07)

Barycentrics    (sin A)f(A,B,C) : (sin B)f(B,C,A) : (sin C)f(C,A,B)
Barycentrics    b2 + c2 - a2 - 4σ) : c2 + a2 - b2 - 4σ) : a2 + b2 - c2 - 4σ)       (M. Iliev, 5/13/07)

X(491) is a pole associated with squares that circumscribe ABC. For details and reference, see X(488). (Floor van Lamoen, 4/26/98)

X(491) lies on these lines: 2,6    3,490    4,487    5,637    76,485    315,371    372,642    488,631

X(491) = isotomic conjugate of X(486)
X(491) = anticomplement of X(615)
X(491) = X(264)-Ceva conjugate of X(492)
X(491) = cevapoint of X(2) and X(487)

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