X3116

ISOGONAL CONJUGATE OF GtX(31)

X3116 is the isogonal conjugate of gtx(31).
< A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 31, 48 }: Central Line L(31, 48) { 38, 75 }: Central Line L(38, 75) { 99, 723 }: Central Line L(99, 723) { 1, 1581 }: Central Line L(1, 1581) { 210, 1575 }: Central Line L(210, 1575) { 63, 1740 }: Central Line L(63, 1740) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_2186 = -ISOCONJUGATE OF X(182) (0.6123, 0.3199) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5412, 0.1246) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_99 = STEINER POINT (0.1109, 0.4322) X_723 = EVEN (- 3, 3) CIRCUMCIRCLE POINT (1.0071, 0.0449) X_1 = INCENTER (0.5714, 0.2333) X_1581 = ISOGONAL CONJUGATE OF X(1580) (1.0304, 0.0330) X_210 = -CEVA CONJUGATE OF X(37) (0.4925, 0.1466) X_1575 = EXSIMILICENTER OF SPIEKER AND (1/2)-MOSES CIRCLES (2.5675, 1.8684) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_1740 = MIMOSA TRANSFORM OF X(184) (0.7017, 0.3500) X_3116 = ISOGONAL CONJUGATE OF GtX(31) (0.5881, 0.2260) A B C X75 X2186 X31 X48 X38 X99 X723 X1 X1581 X210 X1575 X63 X1740 X3116 (a, b, c) = (5, 6, 7) | AB = 1

X3116 (ISOGONAL CONJUGATE OF GtX(31)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a^{2}(b^{6} - c^{6})/(b^{2} - c^{2})\)
Search Value (6, 9, 13): \(1.376631792799\)
▸ Incident Central Lines8 lines

{1, 1581}, {31, 48}, {38, 75}, {63, 1740}, {99, 723}, {210, 1575}, {982, 2887}, {1932, 2172}

▸ Functional Relations3 relations