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

Trilinears

\(1/(1 + sec A) : 1/(1 + sec B) : 1/(1 + sec C)\)

\(cos A sec2(A/2) : cos B sec2(B/2) : cos C sec2(C/2)\)

\((b2 + c2 - a2)/(b + c - a) : :\)

\(SA(SA - bc) : :\)

Barycentrics

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

\(cot A (1 - cos A) : : In the plane of a triangle ABC, let\)

Notes

In the plane of a triangle ABC, let Ia = line through X(7) parallel to BC, and define Ib and Ic cyclically. Ac = Ia∩AB, and define Ba and Cb cyclically. Ab = Ia∩AC, and define Bc and Ca cyclically. Oa = circumcircle of A, Bc, Cb, and define Ob and Oc cyclically. Then

X(77) = radical center of Oa, Ob, Oc. See also X(77). (Ivan Pavlov, April 1, 2022)

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) = trilinear pole of line X(652)X(905)

X(77) = {X(175),:ref:X(176) <X(176)>}-harmonic conjugate of X(962)

X(77) = X(92)-isoconjugate of X(41)

X(77) = perspector of ABC and extraversion triangle of X(78)

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)