X3425

X2-VERTEX CONJUGATE OF X4

X3425 = isogonal conjugate of X1352
< 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) { 22, 184 }: Central Line L(22, 184) { 32, 232 }: Central Line L(32, 232) { 3, 315 }: Central Line L(3, 315) { 98, 264 }: Central Line L(98, 264) { 523, 878 }: Central Line L(523, 878) { 2, 2351 }: Central Line L(2, 2351) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1352 = REFLECTION OF X(6) IN X(5) (0.5122, 0.2306) X_22 = EXETER POINT (0.4143, -0.1221) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_232 = -CEVA CONJUGATE OF X(132) (0.6919, 0.7779) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_315 = ISOTOMIC CONJUGATE OF X(66) (0.3323, -0.0666) X_98 = TARRY POINT (0.8891, -0.2281) X_264 = ISOTOMIC CONJUGATE OF CIRCUMCENTER (0.5720, 0.3293) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_878 = ISOGONAL CONJUGATE OF X(877) (1.1192, 0.0431) X_2 = CENTROID (0.5374, 0.2000) X_2351 = -ISOCONJUGATE OF X(1748) (-0.0825, -0.0111) X_3425 = -VERTEX CONJUGATE OF X(4) (0.6280, 0.2308) A B C X1352 X22 X184 X32 X232 X3 X315 X98 X264 X523 X878 X2 X2351 X3425 (a, b, c) = (5, 6, 7) | AB = 1

X3425 (X2-VERTEX CONJUGATE OF X4) 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 \(x : y : z\) = X4
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(8.143087580543\)
▸ Alternate Coordinates1 form

  • Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = a^{2}/[a^{6} - a^{4}(b^{2} + c^{2}) + a^{2}(b^{2} + c^{2})^{2} - (b^{2} + c^{2})(b^{2} - c^{2})^{2}] (E\). Danneels)

▸ Incident Central Lines8 lines

{2, 2351}, {3, 315}, {4, 2353}, {22, 184}, {32, 232}, {98, 264}, {378, 2794}, {523, 878}

▸ Functional Relations1 relation