X1452

X406-BETH CONJUGATE OF X406

< 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) { 1, 24 }: Central Line L(1, 24) { 4, 46 }: Central Line L(4, 46) { 28, 34 }: Central Line L(28, 34) { 33, 40 }: Central Line L(33, 40) { 25, 65 }: Central Line L(25, 65) { 19, 208 }: Central Line L(19, 208) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_406 = EULER LINE INTERCEPT OF LINE X(10)X(33) (0.5745, 0.2970) X_1 = INCENTER (0.5714, 0.2333) X_24 = PERSPECTOR OF ABC AND ORTHIC-OF-ORTHIC TRIANGLE (0.6627, 0.5278) X_4 = ORTHOCENTER (0.6122, 0.3958) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_28 = CEVAPOINT OF X(19) AND X(25) (0.6285, 0.4382) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_40 = BEVAN POINT (0.4286, -0.0292) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_19 = CLAWSON POINT (0.6246, 0.4244) X_208 = -CEVA CONJUGATE OF X(34) (0.6242, -0.2728) X_1452 = -BETH CONJUGATE OF X(406) (0.6246, 0.4049) A B C X406 X1 X24 X4 X46 X28 X34 X33 X40 X25 X65 X19 X208 X1452 (a, b, c) = (5, 6, 7) | AB = 1

X1452 (X406-BETH CONJUGATE OF X406) 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 \(f(a,b,c) = (1 - \cos A)u(a,b,c)\), where \(u : v : w\) = X406
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(1.863827647536\)
▸ Incident Central Lines8 lines

{1, 24}, {4, 46}, {19, 208}, {25, 65}, {28, 34}, {33, 40}, {227, 607}, {1038, 1039}