X3455

X13-VERTEX CONJUGATE OF X14

X3455 = isogonal conjugate of X316
< 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) circumcircle: Circumcircle of △ABC { 3, 67 }: Central Line L(3, 67) { 25, 115 }: Central Line L(25, 115) { 98, 186 }: Central Line L(98, 186) { 22, 543 }: Central Line L(22, 543) { 23, 671 }: Central Line L(23, 671) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_67 = ISOGONAL CONJUGATE OF X(23) (0.7606, -0.2152) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_115 = CENTER OF KIEPERT HYPERBOLA (0.7507, 0.0838) X_98 = TARRY POINT (0.8891, -0.2281) X_186 = INVERSE-IN-CIRCUMCIRCLE OF X(4) (0.7957, 0.8758) X_22 = EXETER POINT (0.4143, -0.1221) X_543 = DIRECTION OF VECTOR AX + BX + CX, where X = X(99) (0.0220, 0.4806) X_23 = FAR-OUT POINT (1.3871, 2.4232) X_671 = TRILINEAR POLE OF LINE X(2)X(523) (0.9639, -0.0323) X_3455 = -VERTEX CONJUGATE OF X(14) (0.9026, -0.3880) A B C X3 X67 X25 X115 X98 X186 X22 X543 X23 X671 X3455 (a, b, c) = (5, 6, 7) | AB = 1

X3455 (X13-VERTEX CONJUGATE OF X14) 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 \(u : v : w\) = X13 and \(x : y : z\) = X14
Barycentrics: \(a^{2}/(a^{4} - b^{4} - c^{4} + b^{2} c^{2}) : :\)
Search Value (6, 9, 13): \(-21.328507279093\)
▸ Incident Central Lines12 lines

{3, 67}, {22, 543}, {23, 671}, {25, 115}, {39, 1576}, {98, 186}, {99, 1799}, {184, 574}, {187, 2393}, {228, 2157}, {378, 2794}, {1976, 2088}

▸ Functional Relations7 relations

Notes

Let a’ be the line through A tangent to the circle {{A, X3, X6}}, and define b’ and c’ cyclically. The lines a’, b’, c’ concur in X3455. (César Lozada, January 5, 2021)