## X(57) (ISOGONAL CONJUGATE OF X(9))

 Interactive Applet

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 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears           1/(b + c - a) : 1/(c + a - b) : 1/(a + b - c)
= tan(A/2) : tan(B/2) : tan(C/2)

Barycentrics    a/(b + c - a) : b/(c + a - b) : c/(a + b - c)

X(57) is the perspector of the intouch triangle and excentral triangle.

X(57) lies on these lines:
1,3    2,7    4,84    6,222    10,388    19,196    20,938    27,273    28,34    31,105    33,103    38,612    42,1002    43,181    72,474    73,386    77,81    78,404    79,90    85,274    88,651    92,653    164,177    169,277    173,174    200,518    201,975    234,362    239,330    255,580    279,479    345,728    497,516    499,920    649,1024    658,673    748,896    758,997    955,991    957,995    959,1042    961,1106    978,1046    1020,1086

X(57) is the {X(2),X(7)}-harmonic conjugate of X(226).

X(57) = reflection of X(I) in X(J) for these (I,J): (1,999), (200,1376)
X(57) = isogonal conjugate of X(9)
X(57) = isotomic conjugate of X(312)
X(57) = inverse-in-Bevan-circle of X(1155)
X(57) = complement of X(329)

X(57) = X(I)-Ceva conjugate of X(J) for these (I,J):
(2,223), (7,1), (27,278), (81,222), (85,77), (273,34), (279,269)

X(57) = cevapoint of X(I) and X(J) for these (I,J): (6,56), (19,208)
X(57) = X(I)-cross conjugate of X(J) for these (I,J): (6,1), (19,84), (56,269), (65,7)
X(57) = crosspoint of X(I) and X(J) for these (I,J): (2,189), (7,279), (27,81), (85,273)

X(57) = crosssum of X(I) and X(J) for these (I,J): (1,165), (6,198), (31,205), (37,71), (41,212), (55,220), (210,1334)

X(57) = crossdifference of any two points on line X(650)X(663)
X(57) = X(I)-Hirst inverse of X(J) for these (I,J): (1,241), (7,1447), (56,1429), (105,1462), (910,1419)

X(57) = X(I)-aleph conjugate of X(J) for these (I,J):
(2,40), (7,57), (57,978), (174,1), (366,165), (507,503), (508,9), (509,43)

X(57) = X(I)-beth conjugate of X(J) for these (I,J):
(2,2), (81,57), (88,57), (100,57), (110,31), (162,57), (190,57), (333,63), (648,92), (651,57), (653,57), (655,57), (658,57), (660,57), (662,57), (673,57), (771,57), (799,57), (823,57), (897,57)

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