X2409

GIBERT-SIMSON TRANSFORM OF X112

X2409 = crosspoint of X107 and X685
< 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, 3 }: Euler Line { 107, 112 }: Central Line L(107, 112) { 110, 1289 }: Central Line L(110, 1289) { 99, 1301 }: Central Line L(99, 1301) { 935, 1304 }: Central Line L(935, 1304) { 250, 2407 }: Central Line L(250, 2407) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2435 = ISOGONAL CONJUGATE OF X(2409) (2.8968, 0.1781) X_2 = CENTROID (0.5374, 0.2000) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_107 = Ψ(SYMMEDIAN POINT, ORTHOCENTER) (0.5733, 0.6071) X_112 = Ψ(ORTHOCENTER, SYMMEDIAN POINT) (0.5162, 0.6121) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_1289 = COLLINGS TRANSFORM OF X(25) (0.6436, 0.5918) X_99 = STEINER POINT (0.1109, 0.4322) X_1301 = COLLINGS TRANSFORM OF X(235) (0.6568, 0.5877) X_935 = POINT ALCOR (0.8281, 0.4929) X_1304 = COLLINGS TRANSFORM OF X(403) (0.7822, 0.5273) X_250 = ISOGONAL CONJUGATE OF X(125) (0.5892, 0.5347) X_2407 = GIBERT-SIMSON TRANSFORM OF X(110) (1.2056, 0.9180) X_2409 = GIBERT-SIMSON TRANSFORM OF X(112) (0.6891, 0.5969) A B C X2435 X2 X3 X107 X112 X110 X1289 X99 X1301 X935 X1304 X250 X2407 X2409 (a, b, c) = (5, 6, 7) | AB = 1

X2409 (GIBERT-SIMSON TRANSFORM OF X112) 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): \(0.366800468998\)

X2409 lies on the cubic K010.

▸ Incident Central Lines7 lines

{2, 3}, {99, 1301}, {107, 112}, {110, 1289}, {250, 2407}, {685, 2395}, {935, 1304}

▸ Functional Relations8 relations

Notes

As a point on the Euler line, X2409 has Shinagawa coefficients \((6(E + F)F^{2} - 2FS^{2}, -4F(E + F)^{2} + (E + 4F)S^{2})\).