X(43) = X(6)-CEVA CONJUGATE OF X(1)

Trilinears

\(ab + ac - bc : bc + ba - ca : ca + cb - ab\)

\(csc B + csc C - csc A : csc C + csc A - csc B : csc A + csc B - csc C\)

Barycentrics

\(a(ab + ac - bc) : b(bc + ba - ca) : c(ca + cb - ab) Let A' be the inverse-in-excircles-radical-circle of the midpoint of BC, and define B' and C' cyclically. Triangle A'B'C' is inscribed in the Apollonius circle and homothetic to the excentral triangle at :ref:`X(43) <X(43)>\). (Randy Hutson, November 30, 2018) X(43) lies on the Kiepert hyperbola of the excentral triangle and these lines: 1,2 6,87 9,256 31,100 35,1011 40,970 46,851 55,238 57,181 58,979 72,986 75,872 81,750 165,573 170,218 210,984 312,740 518,982 X(43) is the {X(2),:ref:X(42) <X(42)>}-harmonic conjugate of X(1). For a list of other harmonic conjugates of X(43), click Tables at the top of this page. X(43) is the external center of similitude of the Bevan circle and Apollonius circle; the internal center is X(1695). X(43) = reflection of X(1) in X(995) <X(995)>`

Notes

Let A’ be the inverse-in-excircles-radical-circle of the midpoint of BC, and define B’ and C’ cyclically. Triangle A’B’C’ is inscribed in the Apollonius circle and homothetic to the excentral triangle at X(43). (Randy Hutson, November 30, 2018)

X(43) lies on the Kiepert hyperbola of the excentral triangle and these lines: 1,2 6,87 9,256 31,100 35,1011 40,970 46,851 55,238 57,181 58,979 72,986 75,872 81,750 165,573 170,218 210,984 312,740 518,982

X(43) is the {X(2),:ref:X(42) <X(42)>}-harmonic conjugate of X(1). For a list of other harmonic conjugates of X(43), click Tables at the top of this page. X(43) is the external center of similitude of the Bevan circle and Apollonius circle; the internal center is X(1695).

X(43) = reflection of X(1) in X(995)

X(43) = isogonal conjugate of X(87)

X(43) = isotomic conjugate of X(6384)

X(43) = anticomplement of X(3840)

X(43) = X(6)-Ceva conjugate of X(1)

X(43) = X(192)-cross conjugate of X(1)

X(43) = crosssum of X(2) and X(330)

X(43) = X(55)-Hirst inverse of X(238)

X(43) = inverse-in-excircles-radical-circle of X(5121)

X(43) = perspector of ABC and extraversion triangle of X(87)

X(43) = trilinear product of extraversions of X(87)

X(43) = excentral-isogonal conjugate of X(1766)

X(43) = polar conjugate of isotomic conjugate of X(22370)

X(43) = perspector of Gemini triangle 5 and cross-triangle of Gemini triangles 3 and 5

X(43) = X(i)-aleph conjugate of X(j) for these (i,j): (1,9), (6,43), (55,170), (100,1018), (174,169), (259,165), (365,1), (366,63), (507,362), (509,57)

X(43) = X(660)-beth conjugate of X(43)

X(43) = {X(2),:ref:X(8) <X(8)>}-harmonic conjugate of X(3741)