X(85) = X(85) ISOTOMIC CONJUGATE OF X(9)

Trilinears

\(b2c2/(b + c - a) : c2a2/(c + a - b) : a2b2/(a + b - c)\)

Barycentrics

\(bc/(b + c - a) : ca/(c + a - b) : ab/(a + b - c)\)

\(cot A' : :, where A'B'C' is the excentral triangle Let A38B38C38 be Gemini triangle 38. Let A' be the perspector of conic {A,B,C,B38,C38}}, and define B' and C' cyclically. The lines AA', BB', CC' concur in :ref:`X(85) <X(85)>\). (Randy Hutson, January 15, 2019) X(85) lies on these lines: 1,664 2,241 7,8 12,120 29,34 56,870 57,274 76,226 92,331 109,767 150,355 264,309 X(85) = isogonal conjugate of X(41) <X(41)>`

Notes

Let A38B38C38 be Gemini triangle 38. Let A’ be the perspector of conic {A,B,C,B38,C38}}, and define B’ and C’ cyclically. The lines AA’, BB’, CC’ concur in X(85). (Randy Hutson, January 15, 2019)

X(85) lies on these lines: 1,664 2,241 7,8 12,120 29,34 56,870 57,274 76,226 92,331 109,767 150,355 264,309

X(85) = isogonal conjugate of X(41)

X(85) = isotomic conjugate of X(9)

X(85) = complement of X(3177)

X(85) = anticomplement of X(1212)

X(85) = X(274)-Ceva conjugate of X(348)

X(85) = cevapoint of X(i) and X(j) for these (i,j): (1,169), (2,7), (57,77), (92,342)

X(85) = X(i)-cross conjugate of X(j) for these (i,j): (2,75), (57,273), (92,309), (142,2), (226,7)

X(85) = X(i)-beth conjugate of X(j) for these (i,j): (76,76), (85,279), (99,1), (274,85), (668,85), (789,85), (799,85), (811,85)

X(85) = trilinear pole of line X(522)X(693) (the isotomic conjugate of the circumconic centered at X(1), conic {A,B,C,:ref:X(100) <X(100)>,:ref:X(664) <X(664)>,:ref:X(1120) <X(1120)>,:ref:X(1320) <X(1320)>}; also the polar of X(33) wrt polar circle)

X(85) = pole wrt polar circle of trilinear polar of X(33) (line X(657)X(4041))

X(85) = polar conjugate of X(33)

X(85) = {X(7),:ref:X(8) <X(8)>}-harmonic conjugate of X(6604)

X(85) = trilinear square of X(508)

X(85) = trilinear product of vertices of Gemini triangle 9

X(85) = trilinear product of vertices of Gemini triangle 10