## X(651) (TRILINEAR POLE OF LINE X(1)X(3))

 Interactive Applet

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 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears            1/(cos B - cos C) : 1/(cos C - cos A) : 1/(cos A - cos B)
= 1/[(b - c)(b + c - a)] : 1/[(c - a)(c + a - b)] : 1[(a - b)(a + b - c)]
Barycentrics    (sin A)/(cos B - cos C) : (sin B)/(cos C - cos A) : (sin C)/(cos A - cos B)
= a/[(b - c)(b + c - a)] : b/[(c - a)(c + a - b)] : c/[(a - b)(a + b - c)]

X(651) lies on these lines:
2,222    6,7    8,221    9,77    21,73    44,241    57,88    59,513    63,223    65,895    69,478    81,226    100,109    101,934    108,110    144,219    155,1068    190,644    193,608    218,279    255,411    287,894    329,394    404,603    500,943    514,655    645,799    648,823    978,1106

X(651) = isogonal conjugate of X(650)
X(651) = cevapoint of X(101) and X(109)
X(651) = X(I)-cross conjugate of X(J) for these (I,J): (6,59), (101,100), (513,7), (514,81), (521,77)
X(651) = crosssum of X(I) and X(J) for these (I,J): (647,661), (657,663)

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