X(89) = ISOGONAL CONJUGATE OF X(45)

Trilinears

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

Barycentrics

\(a/(2b + 2c - a) : b/(2c + 2a - b) : c/(2a + 2b - c) Let A9B9C9 be the Gemini triangle 9. Let LA be the line through A9 parallel to BC, and define LB and LC cyclically. Let A'9 = LB&cap;LC, and define B'9, C'9 cyclically. Triangle A'9B'9C'9 is homothetic to ABC at :ref:`X(89) <X(89)>\). (Randy Hutson, November 30, 2018) X(89) lies on these lines: 1,902 2,44 6,88 649,1022 X(89) = isogonal conjugate of X(45) <X(45)>`

Notes

Let A9B9C9 be the Gemini triangle 9. Let LA be the line through A9 parallel to BC, and define LB and LC cyclically. Let A’9 = LB&cap;LC, and define B’9, C’9 cyclically. Triangle A’9B’9C’9 is homothetic to ABC at X(89). (Randy Hutson, November 30, 2018)

X(89) lies on these lines: 1,902 2,44 6,88 649,1022

X(89) = isogonal conjugate of X(45)

X(89) = isotomic conjugate of X(4671)

X(89) = anticomplement of isotomic conjugate of isogonal conjugate of X(20973)

X(89) = anticomplement of polar conjugate of isogonal conjugate of X(22083)

X(89) = anticomplement of complementary conjugate of X(34824)