X(34) = X(4)-BETH CONJUGATE OF X(4)

Trilinears

\(1 - sec A : 1 - sec B : 1 - sec C\)

\(tan A tan(A/2) : tan B tan(B/2) : tan C tan(C/2)\)

\(1/[(b + c - a)(b2 + c2 - a2)] : :\)

\(sec A sin2(A/2)\)

Barycentrics

\(sin A - tan A : sin B - tan B : sin C - tan C\)

\(tan A sin2(A/2) : :\)

Notes

X(34) is the center of perspective of the orthic triangle and the reflection in the incenter of the intangents triangle.

If you have The Geometer’s Sketchpad, you can view X(34) (1) and X(34) (2).

X(34) lies on these lines: 1,4 2,1038 5,1060 6,19 7,1039 8,1041 9,201 10,475 11,235 12,427 20,1040 24,36 25,56 28,57 29,77 30,1062 35,378 40,212 46,47 55,227 79,1061 80,1063 87,242 106,108 196,937 207,1042 222,942 244,1106 331,870 347,452 860,997

X(34) is the {X(1),:ref:X(4) <X(4)>}-harmonic conjugate of X(33). For a list of other harmonic conjugates of X(34), click Tables at the top of this page.

X(34) = isogonal conjugate of X(78)

X(34) = isotomic conjugate of X(3718)

X(34) = anticomplement of X(34823)

X(34) = X(i)-Ceva conjugate of X(j) for these (i,j): (1,207), (4,208), (28,56), (273,57), (278,19)

X(34) = X(25)-cross conjugate of X(19)

X(34) = crosssum of X(219) and X(1260)

X(34) = crossdifference of every pair of points on line X(521)X(652)

X(34) = circumcircle-inverse of X(32757)

X(34) = X(56)-Hirst inverse of X(1430)

X(34) = trilinear pole of polar of X(312) wrt polar circle (line X(649)X(4017))

X(34) = pole wrt polar circle of trilinear polar of X(312) (line X(522)X(3717))

X(34) = polar conjugate of X(312)

X(34) = perspector of ABC and extraversion triangle of X(33)

X(34) = homothetic center of intangents triangle and reflection of orthic triangle in X(4)

X(34) = homothetic center of orthic triangle and anti-tangential midarc triangle

X(34) = X(8078)-of-orthic-triangle if ABC is acute

X(34) = X(i)-beth conjugate of X(j) for these (i,j): (1,221), (4,4), (28,34), (29,1), (107,158), (108,34), (110,47), (162,34), (811,34)

X(34) = X(i)-isoconjugate of X(j) for these {i,j}: {1,78}, {31,3718}, {48,312}