X3427

X3-VERTEX CONJUGATE OF X7

X3427 = isogonal conjugate of X3428
< 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) { 9, 515 }: Central Line L(9, 515) { 104, 1617 }: Central Line L(104, 1617) { 943, 944 }: Central Line L(943, 944) { 1156, 2829 }: Central Line L(1156, 2829) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3428 = ISOGONAL CONJUGATE OF X(3427) (0.4510, 0.0120) X_9 = MITTENPUNKT (0.5110, 0.1615) X_515 = ISOGONAL CONJUGATE OF X(102) (0.6804, 0.7691) X_104 = ANTIPODE OF X(100) (0.8571, -0.2624) X_1617 = TCC-PERSPECTOR OF X(57) (0.6629, 0.4014) X_943 = ISOGONAL CONJUGATE OF X(942) (0.5528, 0.2043) X_944 = HOFSTADTER TRAPEZOID POINT (0.5306, 0.0708) X_1156 = ISOGONAL CONJUGATE OF X(1155) (0.8791, -0.1436) X_2829 = ISOGONAL CONJUGATE OF X(2745) (0.3328, 0.7500) X_3427 = -VERTEX CONJUGATE OF X(7) (0.6136, 0.5700) A B C X3428 X9 X515 X104 X1617 X943 X944 X1156 X2829 X3427 (a, b, c) = (5, 6, 7) | AB = 1

X3427 (X3-VERTEX CONJUGATE OF X7) 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 \(u : v : w\) = X3 and \(x : y : z\) = X7
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-30.890009760136\)
▸ Alternate Coordinates1 form

  • Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = 1/[a^{5} - a^{4}(b + c) - 2a^{3}(b^{2} + c^{2}) + 2a^{2}(b + c)(b - c)^{2} + a(b^{4} + 6b^{2}c^{2} + c^{4}) - (b + c)(b - c)^{4}] (E\). Danneels)

▸ Incident Central Lines4 lines

{9, 515}, {104, 1617}, {943, 944}, {1156, 2829}

▸ Functional Relations1 relation