X1430

X243-BETH CONJUGATE OF X243

X1430 = X34-Hirst inverse of X56
< 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) { 25, 34 }: Central Line L(25, 34) { 27, 58 }: Central Line L(27, 58) { 92, 171 }: Central Line L(92, 171) { 31, 278 }: Central Line L(31, 278) { 162, 238 }: Central Line L(162, 238) { 1, 1013 }: Central Line L(1, 1013) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_243 = -LINE CONJUGATE OF X(73) (0.7516, 0.9505) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_27 = CEVAPOINT OF ORTHOCENTER AND CLAWSON CENTER (0.6182, 0.4112) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_92 = CEVAPOINT OF INCENTER AND CLAWSON POINT (0.5949, 0.3639) X_171 = {X(2), X(31)}-HARMONIC CONJUGATE OF X(238) (0.5819, 0.2525) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_278 = ISOGONAL CONJUGATE OF X(219) (0.6278, 0.4577) X_162 = CEVAPOINT OF X(108) AND X(109) (0.4897, 0.6018) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_1 = INCENTER (0.5714, 0.2333) X_1013 = INTERCEPT OF EULER LINE AND LINE X(7)X(108) (0.5829, 0.3190) X_1430 = -BETH CONJUGATE OF X(243) (0.6360, 0.7152) A B C X243 X25 X34 X27 X58 X92 X171 X31 X278 X162 X238 X1 X1013 X1430 (a, b, c) = (5, 6, 7) | AB = 1

X1430 (X243-BETH CONJUGATE OF X243) 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 \(u : v : w\) = X243
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.234670219420\)
▸ Incident Central Lines11 lines

{1, 1013}, {4, 1468}, {25, 34}, {27, 58}, {31, 278}, {57, 1096}, {92, 171}, {108, 1458}, {162, 238}, {281, 750}, {603, 1118}

▸ Functional Relations1 relation