X1460

X612-BETH CONJUGATE OF X612

X1460 = isogonal conjugate of X30479
< 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, 3 }: OI Line (Incenter–Circumcenter Line) { 25, 31 }: Central Line L(25, 31) { 6, 181 }: Central Line L(6, 181) { 42, 604 }: Central Line L(42, 604) { 8, 961 }: Central Line L(8, 961) { 332, 1014 }: Central Line L(332, 1014) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_612 = INTERSECTION OF LINES X(1)X(2) AND X(9)X(31) (0.5582, 0.2203) X_1 = INCENTER (0.5714, 0.2333) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_181 = APOLLONIUS POINT (0.6163, 0.3093) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_604 = -CEVA CONJUGATE OF X(31) (0.6442, 0.3744) X_8 = NAGEL POINT (0.4694, 0.1333) X_961 = ISOGONAL CONJUGATE OF X(960) (0.6167, 0.3210) X_332 = ISOTOMIC CONJUGATE OF X(225) (0.3595, 0.0434) X_1014 = ISOGONAL CONJUGATE OF X(210) (0.6222, 0.3285) X_1460 = -BETH CONJUGATE OF X(612) (0.6249, 0.3315) A B C X612 X1 X3 X25 X31 X6 X181 X42 X604 X8 X961 X332 X1014 X1460 (a, b, c) = (5, 6, 7) | AB = 1

X1460 (X612-BETH CONJUGATE OF X612) 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 \(u : v : w\) = X612
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.242594851685\)
▸ Incident Central Lines11 lines

{1, 3}, {6, 181}, {8, 961}, {25, 31}, {42, 604}, {222, 1469}, {332, 1014}, {388, 1010}, {959, 1036}, {1254, 1398}, {1401, 1407}

▸ Functional Relations2 relations