X1473

X1040-BETH CONJUGATE OF X1040

X1473 = X101-Ceva conjugate of X1459
< 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) { 3, 63 }: Central Line L(3, 63) { 25, 57 }: Central Line L(25, 57) { 31, 56 }: Central Line L(31, 56) { 38, 55 }: Central Line L(38, 55) { 184, 222 }: Central Line L(184, 222) { 198, 672 }: Central Line L(198, 672) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1040 = INTERSECTION OF LINES X(1)X(3) AND X(2)X(33) (0.4854, 0.0753) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_222 = -CEVA CONJUGATE OF X(56) (0.5653, 0.1568) X_198 = -CEVA CONJUGATE OF X(6) (0.4741, -0.0381) X_672 = CROSSDIFFERENCE OF X(1) AND X(514) (1.9245, 2.2184) X_1473 = -BETH CONJUGATE OF X(1040) (0.5906, 0.1432) A B C X1040 X3 X63 X25 X57 X31 X56 X38 X55 X184 X222 X198 X672 X1473 (a, b, c) = (5, 6, 7) | AB = 1

X1473 (X1040-BETH CONJUGATE OF X1040) 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 \(u : v : w\) = X1040
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(22.243767032210\)
▸ Incident Central Lines9 lines

{3, 63}, {25, 57}, {31, 56}, {38, 55}, {184, 222}, {197, 1155}, {198, 672}, {988, 1036}, {1394, 1398}

▸ Functional Relations2 relations