X2407

GIBERT-SIMSON TRANSFORM OF X110

X2407 = X1637-cross conjugate of X30
< 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, 6 }: Centroid–Symmedian Line { 99, 112 }: Central Line L(99, 112) { 98, 895 }: Central Line L(98, 895) { 110, 1302 }: Central Line L(110, 1302) { 892, 2395 }: Central Line L(892, 2395) { 1723, 2358 }: Central Line L(1723, 2358) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2433 = ISOGONAL CONJUGATE OF X(2407) (1.1401, 0.1425) X_2 = CENTROID (0.5374, 0.2000) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_99 = STEINER POINT (0.1109, 0.4322) X_112 = Ψ(ORTHOCENTER, SYMMEDIAN POINT) (0.5162, 0.6121) X_98 = TARRY POINT (0.8891, -0.2281) X_895 = ISOGONAL CONJUGATE OF X(468) (0.9484, -0.0134) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_1302 = COLLINGS TRANSFORM OF X(381) (0.3827, 0.5987) X_892 = ISOGONAL CONJUGATE OF X(351) (1.0590, 0.0699) X_2395 = GIBERT-SIMSON TRANSFORM OF X(98) (1.0626, 0.0904) X_1723 = MIMOSA TRANSFORM OF X(57) (0.7970, 0.5012) X_2358 = -ISOCONJUGATE OF X(1819) (0.6083, 0.6139) X_2407 = GIBERT-SIMSON TRANSFORM OF X(110) (1.2056, 0.9180) A B C X2433 X2 X6 X99 X112 X98 X895 X110 X1302 X892 X2395 X1723 X2358 X2407 (a, b, c) = (5, 6, 7) | AB = 1

X2407 (GIBERT-SIMSON TRANSFORM OF X110) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((\csc(C - A) \cos C - \csc(A - B) \cos B)(\csc(B - C)/a)^{2} : :\)
Barycentrics: \((2 a^{4} - b^{4} - c^{4} - a^{2} b^{2} - a^{2} c^{2} + 2 b^{2} c^{2})/(b^{2} - c^{2}) : :\)
Search Value (6, 9, 13): \(-1.619397290372\)
▸ Alternate Coordinates1 form

  • Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where f(a,b,c) is as given just before X2394

X2407 lies on the cubic K010.

▸ Incident Central Lines10 lines

{2, 6}, {98, 895}, {99, 112}, {110, 1302}, {249, 2411}, {250, 2409}, {691, 2408}, {892, 2395}, {1723, 2358}, {2394, 2410}

▸ Functional Relations9 relations