X2414

GIBERT-SIMSON TRANSFORM OF X1292

X2414 = trilinear pole of line X120X518 (the Simson line of X1292)
< 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, 277 }: Central Line L(2, 277) { 100, 1292 }: Central Line L(100, 1292) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2440 = ISOGONAL CONJUGATE OF X(2414) (0.9796, 0.0606) X_2 = CENTROID (0.5374, 0.2000) X_277 = ISOGONAL CONJUGATE OF X(218) (0.4242, 0.1335) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_1292 = COLLINGS TRANSFORM OF X(55) (0.0286, 0.2974) X_2414 = GIBERT-SIMSON TRANSFORM OF X(1292) (-0.4153, -0.3594) A B C X2440 X2 X277 X100 X1292 X2414 (a, b, c) = (5, 6, 7) | AB = 1

X2414 (GIBERT-SIMSON TRANSFORM OF X1292) 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): \(6.304814912152\)

X2414 lies on the cubic K010.

▸ Incident Central Lines2 lines

{2, 277}, {100, 1292}

▸ Functional Relations3 relations