X1465

X908-BETH CONJUGATE OF X908

X1465 = X1361-cross conjugate of X7
< 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, 34 }: Central Line L(3, 34) { 6, 57 }: Central Line L(6, 57) { 2, 92 }: Central Line L(2, 92) { 1, 227 }: Central Line L(1, 227) { 5, 225 }: Central Line L(5, 225) { 46, 221 }: Central Line L(46, 221) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_908 = POINT ACUBENS (-0.8367, -1.7996) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_2 = CENTROID (0.5374, 0.2000) X_92 = CEVAPOINT OF INCENTER AND CLAWSON POINT (0.5949, 0.3639) X_1 = INCENTER (0.5714, 0.2333) X_227 = -CEVA CONJUGATE OF X(65) (0.4792, -0.0460) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_225 = -CEVA CONJUGATE OF X(65) (0.6246, 0.4451) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_221 = -CEVA CONJUGATE OF X(56) (0.5474, -0.0688) X_1465 = -BETH CONJUGATE OF X(908) (0.7719, 1.0314) A B C X908 X3 X34 X6 X57 X2 X92 X1 X227 X5 X225 X46 X221 X1465 (a, b, c) = (5, 6, 7) | AB = 1

X1465 (X908-BETH CONJUGATE OF X908) 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 \(u : v : w\) = X908
Barycentrics: \((1 - \cos A) ((a - c) \cos B + (a - b) \cos C) : :\)
Search Value (6, 9, 13): \(-0.528446555003\)
▸ Incident Central Lines21 lines

{1, 227}, {2, 92}, {3, 34}, {5, 225}, {6, 57}, {36, 1455}, {46, 221}, {56, 998}, {65, 386}, {73, 942}, {88, 1443}, {106, 1168}, {109, 1155}, {241, 514}, {244, 1458}, {474, 1038}, {517, 1457}, {919, 1462}, {1193, 1254}, {1279, 1421}, {1448, 1466}

▸ Functional Relations6 relations