X2406

GIBERT-SIMSON TRANSFORM OF X109

X2406 = trilinear pole of line X117X515 (the Simson line of X109)
< 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, 7 }: Centroid–Gergonne Line { 651, 653 }: Central Line L(651, 653) { 59, 2398 }: Central Line L(59, 2398) { 655, 2401 }: Central Line L(655, 2401) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2432 = ISOGONAL CONJUGATE OF X(2406) (1.3884, 0.1546) X_2 = CENTROID (0.5374, 0.2000) X_7 = GERGONNE POINT (0.5903, 0.2769) X_651 = TRILINEAR POLE OF LINE X(1)X(3) (0.3048, 0.5599) X_653 = TRILINEAR POLE OF LINE X(1)X(4) (0.5097, 0.6030) X_59 = ISOGONAL CONJUGATE OF X(11) (0.5333, 0.4355) X_2398 = GIBERT-SIMSON TRANSFORM OF X(101) (1.4898, 1.1331) X_655 = TRILINEAR POLE OF LINE X(1)X(5) (1.0449, 0.2400) X_2401 = GIBERT-SIMSON TRANSFORM OF X(104) (1.1020, 0.1000) X_2406 = GIBERT-SIMSON TRANSFORM OF X(109) (0.8660, 0.6781) A B C X2432 X2 X7 X651 X653 X59 X2398 X655 X2401 X2406 (a, b, c) = (5, 6, 7) | AB = 1

X2406 (GIBERT-SIMSON TRANSFORM OF X109) 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): \(-0.271506187721\)

X2406 lies on the cubic K010.

▸ Incident Central Lines4 lines

{2, 7}, {59, 2398}, {651, 653}, {655, 2401}

▸ Functional Relations4 relations