## X(77) (ISOGONAL CONJUGATE OF X(33))

 Interactive Applet

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 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears           1/(1 + sec A) : 1/(1 + sec B) : 1/(1 + sec C)
= cos A sec2(A/2) : cos B sec2(B/2) : cos C sec2(C/2)
= (b2 + c2 - a2)/(b + c - a) : (c2 + a2 - b2)/(c + a - b) : (a2 + b2 - c2)/(a + b - c)

Barycentrics    a/(1 + sec A) : b/(1 + sec B) : c/(1 + sec C)

X(77) lies on these lines:
1,7    2,189    6,241    9,651    29,34    40,947    55,1037    56,1036    57,81    63,219    65,969    69,73    75,664    102,934    283,603    309,318    738,951    988,1106    999,1057

X(77) = isogonal conjugate of X(33)
X(77) = isotomic conjugate of X(318)
X(77) = X(I)-Ceva conjugate of X(J) for these (I,J): (85,57), (86,7), (348,63)
X(77) = cevapoint of X(I) and X(J) for these (I,J): (1,223), (3,222)
X(77) = X(I)-cross conjugate of X(J) for these (I,J): (3,63), (73,222)

X(77) = X(I)-beth conjugate of X(J) for these (I,J):
(21,990), (69,69), (86,269), (99,75), (332,326), (336,77), (662,77), (664,77), (811,77)

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