X(88) = ISOGONAL CONJUGATE OF X(44)¶

Trilinears

\(1/(b + c - 2a) : 1/(c + a - 2b) : 1/(a + b - 2c)\)

Barycentrics

\(a/(b + c - 2a) : b/(c + a - 2b) : c/(a + b - 2c)\)

Notes

Let A9B9C9 be Gemini triangle 9. Let A’ be the perspector of conic {A,B,C,B9,C9}}, and define B’ and C’ cyclically. The lines AA’, BB’, CC’ concur in X(88). (Randy Hutson, January 15, 2019)

See (and hear) Dan Reznik’s Dance of the Swans: X(88) and X(162) and their Never-Touching Motion Over the Elliptic Billiard (March 4, 2020)

X(88) lies on these lines: 1,100 2,45 6,89 28,162 44,679 57,651 81,662 105,901 274,799 278,653 279,658 291,660

X(88) = isogonal conjugate of X(44)

X(88) = isotomic conjugate of X(4358)

X(88) = complement of X(30578)

X(88) = cevapoint of X(i) and X(j) for these (i,j): (1,44), (6,36)

X(88) = X(i)-cross conjugate of X(j) for these (i,j): (44,1), (517,7)

X(88) = X(i)-aleph conjugate of X(j) for these (i,j): (88,1), (679,88), (903,63), (1022,1052)

X(88) = X(333)-beth conjugate of X(190)

X(88) = trilinear product of PU(50)

X(88) = perspector of conic {A,B,C,PU(50)}}

X(88) = trilinear pole of PU(55); the line X(1)X(513), the line through X(1) parallel to its trilinear polar; also normal to Feuerbach hyperbola at X(1)

X(88) = crossdifference of every pair of points on line X(678)X(1635)

X(88) = X(6)-isoconjugate of X(519)

X(88) = BSS(a^2&srarr;a) of X(111)

X(88) = polar conjugate of X(38462)

X(88) = X(19)-isoconjugate of X(5440)

X(88) = X(48)-isoconjugate of X(38462)

X(88) = X(92)-isoconjugate of X(23202)