X1422

X189-BETH CONJUGATE OF X189

X1422 = cevapoint of X1413 and X1436
< 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) { 2, 77 }: Central Line L(2, 77) { 1, 84 }: Central Line L(1, 84) { 269, 278 }: Central Line L(269, 278) { 35, 1079 }: Central Line L(35, 1079) { 34, 1256 }: Central Line L(34, 1256) { 28, 1412 }: Central Line L(28, 1412) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_189 = CYCLOCEVIAN CONJUGATE OF X(8) (0.6131, 0.7055) X_2 = CENTROID (0.5374, 0.2000) X_77 = ISOGONAL CONJUGATE OF X(33) (0.5270, 0.1305) X_1 = INCENTER (0.5714, 0.2333) X_84 = ISOGONAL CONJUGATE OF X(40) (0.6071, 0.6816) X_269 = ISOGONAL CONJUGATE OF X(200) (0.6369, 0.3847) X_278 = ISOGONAL CONJUGATE OF X(219) (0.6278, 0.4577) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_1079 = TRILINEAR SQUARE OF X(46) (0.6490, 0.5422) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_1256 = ISOGONAL CONJUGATE OF X(1103) (0.6135, 0.5942) X_28 = CEVAPOINT OF X(19) AND X(25) (0.6285, 0.4382) X_1412 = -BETH CONJUGATE OF X(81) (0.6374, 0.3603) X_1422 = -BETH CONJUGATE OF X(189) (0.6044, 0.6471) A B C X189 X2 X77 X1 X84 X269 X278 X35 X1079 X34 X1256 X28 X1412 X1422 (a, b, c) = (5, 6, 7) | AB = 1

X1422 (X189-BETH CONJUGATE OF X189) 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 \(u : v : w\) = X189
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.404873986068\)
▸ Incident Central Lines10 lines

{1, 84}, {2, 77}, {28, 1412}, {34, 1256}, {35, 1079}, {57, 1436}, {268, 1214}, {269, 278}, {271, 1257}, {280, 1219}

▸ Functional Relations4 relations