X3428

ISOGONAL CONJUGATE OF X3427

X3428 is the isogonal conjugate of X3427.
< 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, 3434 }: Central Line L(20, 3434) { 1, 3 }: OI Line (Incenter–Circumcenter Line) { 101, 102 }: Central Line L(101, 102) { 8, 411 }: Central Line L(8, 411) { 221, 255 }: Central Line L(221, 255) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_3434 = ISOGONAL CONJUGATE OF X(3433) (0.5142, 0.2156) X_1 = INCENTER (0.5714, 0.2333) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_102 = Λ(INCENTER, ORTHOCENTER) (0.6364, -0.3897) X_8 = NAGEL POINT (0.4694, 0.1333) X_411 = EULER X(21)-2nd-SUBSTITUTION POINT (0.4414, -0.0514) X_221 = -CEVA CONJUGATE OF X(56) (0.5474, -0.0688) X_255 = ISOGONAL CONJUGATE OF X(158) (0.4217, 0.0365) X_3428 = ISOGONAL CONJUGATE OF X(3427) (0.4510, 0.0120) A B C X20 X3434 X1 X3 X101 X102 X8 X411 X221 X255 X3428 (a, b, c) = (5, 6, 7) | AB = 1

X3428 (ISOGONAL CONJUGATE OF X3427) 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 \(f(a,b,c) = 1/x(3427)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(10.929256372256\)
▸ Alternate Coordinates1 form

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

▸ Incident Central Lines22 lines

{1, 3}, {4, 958}, {6, 1064}, {8, 411}, {20, 2894}, {21, 962}, {101, 102}, {104, 376}, {212, 1457}, {221, 255}, {347, 934}, {405, 946}, {516, 993}, {602, 1191}, {859, 2328}, {945, 1794}, {953, 2742}, {1001, 1006}, {1042, 1496}, {1808, 2716}, {1753, 1824}, {2178, 2256}

▸ Functional Relations3 relations