X3424

X2-VERTEX CONJUGATE OF X3

X3424 = isogonal conjugate of X1350
< 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) { 20, 76 }: Central Line L(20, 76) { 2, 154 }: Central Line L(2, 154) { 253, 1297 }: Central Line L(253, 1297) { 193, 1916 }: Central Line L(193, 1916) { 385, 2996 }: Central Line L(385, 2996) { 671, 2794 }: Central Line L(671, 2794) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1350 = REFLECTION OF X(6) IN X(3) (0.4000, -0.0631) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_2 = CENTROID (0.5374, 0.2000) X_154 = -CEVA CONJUGATE OF X(6) (0.4807, -0.3954) X_253 = -CROSS CONJUGATE OF X(2) (3.5087, 32.5688) X_1297 = COLLINGS TRANSFORM OF X(127) (0.4838, -0.4080) X_193 = -CEVA CONJUGATE OF X(2) (0.7878, 0.4690) X_1916 = TRILINEAR POLE OF PU(11) (1.0447, 0.0288) X_385 = -HIRST INVERSE OF X(6) (2.2863, 2.0795) X_2996 = CD(X(25)) (-0.6196, -0.1183) X_671 = TRILINEAR POLE OF LINE X(2)X(523) (0.9639, -0.0323) X_2794 = ISOGONAL CONJUGATE OF X(2710) (0.2994, 0.7364) X_3424 = -VERTEX CONJUGATE OF X(3) (0.5946, 0.8000) A B C X1350 X20 X76 X2 X154 X253 X1297 X193 X1916 X385 X2996 X671 X2794 X3424 (a, b, c) = (5, 6, 7) | AB = 1

X3424 (X2-VERTEX CONJUGATE OF X3) 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 \(f(a,b,c) = a/[a^{2}vwyz - ux(bw + cv)(bz + cy)]\), where \(u : v : w\) = X2 and \(x : y : z\) = X3
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-78.552283677532\)
▸ Alternate Coordinates1 form

  • Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = 1/[a^{4} + 2a^{2}(b^{2} + c^{2}) - 3b^{4} - 3c^{4} - 2b^{2}c^{2}] (E\). Danneels)

▸ Incident Central Lines7 lines

{2, 154}, {20, 76}, {193, 1916}, {253, 1297}, {385, 2996}, {671, 2794}, {1499, 2394}

▸ Functional Relations3 relations