X(1214) (ISOGONAL CONJUGATE OF X(1172))

 Interactive Applet

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 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears           1/f(a,b,c) : 1/f(b,c,a) : 1/f(c,a,b), where f(a,b,c) is as in X(1172)
= cot A (cos B + cos C) : cot B (cos C + cos A) : cot C (cos A + cos B) (Darij Grinberg, 4/11/03)

X(1214) lies on these lines:
1,3    2,92    7,464    9,223    10,227    34,405    37,226    63,77    72,73    216,1108    225,442    304,345    306,307    333,664    343,914

X(1214) = isogonal conjugate of X(1172)
X(1214) = complement of X(92)
X(1214) = X(I)-Ceva conjugate of X(J) for these (I,J) : (2,226), (77,73), (307,72), (348,307)
X(1214) = cevapoint of X(I) and X(J) for these (I,J): (37,227), (71,73)
X(1214) = X(I)-cross conjugate of X(J) for these (I,J): (71,72), (201,307)
X(1214) = crosspoint of X(I) and X(J) for these (I,J): (2,63), (77,348), (1231,1441)
X(1214) = crosssum of X(I) and X(J) for these (I,J): (6,19), (33,607)

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