X1403

X43-BETH CONJUGATE OF X43

X1403 = X604-Ceva conjugate 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) { 1, 3 }: OI Line (Incenter–Circumcenter Line) { 75, 183 }: Central Line L(75, 183) { 109, 727 }: Central Line L(109, 727) { 6, 893 }: Central Line L(6, 893) { 2, 1284 }: Central Line L(2, 1284) { 31, 1428 }: Central Line L(31, 1428) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_1 = INCENTER (0.5714, 0.2333) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_183 = TRILINEAR PRODUCT X(75)X(182) (0.4700, 0.1275) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_727 = EVEN (- 2, -1) CIRCUMCIRCLE POINT (1.0060, 0.1685) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_893 = -CROSS CONJUGATE OF X(292) (0.5910, 0.2480) X_2 = CENTROID (0.5374, 0.2000) X_1284 = 8th SHARYGIN POINT (0.9846, 0.9156) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_1428 = -BETH CONJUGATE OF X(238) (0.5173, 0.1103) X_1403 = -BETH CONJUGATE OF X(43) (0.6606, 0.3972) A B C X43 X1 X3 X75 X183 X109 X727 X6 X893 X2 X1284 X31 X1428 X1403 (a, b, c) = (5, 6, 7) | AB = 1

X1403 (X43-BETH CONJUGATE OF X43) 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 \(u : v : w\) = X43
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.020959929319\)
▸ Incident Central Lines9 lines

{1, 3}, {2, 1284}, {6, 893}, {31, 1428}, {42, 1469}, {43, 1423}, {75, 183}, {109, 727}, {1326, 1412}

▸ Functional Relations7 relations