X2402

GIBERT-SIMSON TRANSFORM OF X105

X2402 = isogonal conjugate of X2428
< 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) { 2, 650 }: Central Line L(2, 650) { 523, 885 }: Central Line L(523, 885) { 514, 1024 }: Central Line L(514, 1024) { 522, 1027 }: Central Line L(522, 1027) { 918, 1814 }: Central Line L(918, 1814) { 666, 2397 }: Central Line L(666, 2397) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2428 = ISOGONAL CONJUGATE OF X(2402) (-1.9546, -1.7457) X_2 = CENTROID (0.5374, 0.2000) X_650 = CROSSDIFFERENCE OF X(1) AND X(3) (13.7143, -4.1991) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_885 = ISOTOMIC CONJUGATE OF X(883) (1.0518, 0.0256) X_514 = ISOGONAL CONJUGATE OF X(101) (1.0761, -0.0329) X_1024 = INTERSECTION OF LINES X(6)X(513) ANDX(9)X(522) (1.0370, 0.0294) X_522 = ISOGONAL CONJUGATE OF X(109) (-0.0318, 0.3430) X_1027 = INTERSECTION OF LINES X(1)X(514) AND X(6)X(513) (1.0130, 0.0424) X_918 = ISOTOMIC CONJUGATE OF X(666) (1.0192, 0.5351) X_1814 = INVERSE MIMOSA TRANSFORM OF X(672) (0.8952, -0.0254) X_666 = TRILINEAR POLE OF LINE X(2)X(11) (1.0982, 0.1428) X_2397 = GIBERT-SIMSON TRANSFORM OF X(100) (4.6735, 3.5993) X_2402 = GIBERT-SIMSON TRANSFORM OF X(105) (0.9981, 0.0461) A B C X2428 X2 X650 X523 X885 X514 X1024 X522 X1027 X918 X1814 X666 X2397 X2402 (a, b, c) = (5, 6, 7) | AB = 1

X2402 (GIBERT-SIMSON TRANSFORM OF X105) 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) is as given just before X2394
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.361449618374\)

X2402 lies on the cubic K010.

▸ Incident Central Lines6 lines

{2, 650}, {514, 1024}, {522, 1027}, {523, 885}, {666, 2397}, {918, 1814}

▸ Functional Relations4 relations