X3423

X1-VERTEX CONJUGATE OF X57

X3423 = isogonal conjugate of X2550
< 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) { 3, 41 }: Central Line L(3, 41) { 25, 57 }: Central Line L(25, 57) { 7, 105 }: Central Line L(7, 105) { 55, 63 }: Central Line L(55, 63) { 31, 222 }: Central Line L(31, 222) { 513, 884 }: Central Line L(513, 884) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2550 = INSIMILICENTER(SPIEKER CIRCLE, (X(4),2R)) (0.5298, 0.2051) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_41 = -CEVA CONJUGATE OF X(31) (0.5823, 0.2244) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_7 = GERGONNE POINT (0.5903, 0.2769) X_105 = Λ(INCENTER, SYMMEDIAN POINT) (0.9714, -0.0933) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_222 = -CEVA CONJUGATE OF X(56) (0.5653, 0.1568) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_884 = ISOGONAL CONJUGATE OF X(883) (1.0241, 0.0337) X_3423 = -VERTEX CONJUGATE OF X(57) (0.6068, 0.2608) A B C X2550 X3 X41 X25 X57 X7 X105 X55 X63 X31 X222 X513 X884 X3423 (a, b, c) = (5, 6, 7) | AB = 1

X3423 (X1-VERTEX CONJUGATE OF X57) 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 \(u : v : w\) = X1 and \(x : y : z\) = X57
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(1.020268724100\)
▸ Alternate Coordinates1 form

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

▸ Incident Central Lines9 lines

{3, 41}, {7, 105}, {25, 57}, {31, 222}, {55, 63}, {513, 884}, {1037, 1362}, {1790, 2194}, {2163, 2291}

▸ Functional Relations1 relation