X2419

GIBERT-SIMSON TRANSFORM OF X1297

X2419 = trilinear pole of line X127X525 (the Simson line of X1297)
< 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) { 253, 523 }: Central Line L(253, 523) { 1297, 2373 }: Central Line L(1297, 2373) { 69, 2435 }: Central Line L(69, 2435) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2445 = ISOGONAL CONJUGATE OF X(2419) (0.6577, 0.5878) X_253 = -CROSS CONJUGATE OF X(2) (3.5087, 32.5688) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_1297 = COLLINGS TRANSFORM OF X(127) (0.4838, -0.4080) X_2373 = CIR(X(67)) (0.5684, -0.4036) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_2435 = ISOGONAL CONJUGATE OF X(2409) (2.8968, 0.1781) X_2419 = GIBERT-SIMSON TRANSFORM OF X(1297) (79.2052, 3.6384) A B C X2445 X253 X523 X1297 X2373 X69 X2435 X2419 (a, b, c) = (5, 6, 7) | AB = 1

X2419 (GIBERT-SIMSON TRANSFORM OF X1297) 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): \(14.115413616795\)

X2419 lies on the cubic K010.

▸ Incident Central Lines4 lines

{2, 3265}, {69, 2435}, {253, 523}, {1297, 2373}

▸ Functional Relations3 relations