X1396

X27-BETH CONJUGATE OF X27

< 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) { 7, 27 }: Central Line L(7, 27) { 28, 34 }: Central Line L(28, 34) { 223, 284 }: Central Line L(223, 284) { 108, 741 }: Central Line L(108, 741) { 4, 940 }: Central Line L(4, 940) { 21, 1214 }: Central Line L(21, 1214) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_27 = CEVAPOINT OF ORTHOCENTER AND CLAWSON CENTER (0.6182, 0.4112) X_7 = GERGONNE POINT (0.5903, 0.2769) X_28 = CEVAPOINT OF X(19) AND X(25) (0.6285, 0.4382) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_223 = -CEVA CONJUGATE OF X(57) (0.4996, -0.0528) X_284 = -CROSS CONJUGATE OF X(21) (0.5646, 0.2088) X_108 = Ψ(CIRCUMCENTER, INCENTER) (0.5320, 0.6114) X_741 = EVEN (- 1, 1) CIRCUMCIRCLE POINT (1.0071, 0.0451) X_4 = ORTHOCENTER (0.6122, 0.3958) X_940 = POINT ALDEBARAN (0.5757, 0.2411) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_1214 = ISOGONAL CONJUGATE OF X(1172) (0.5087, 0.1180) X_1396 = -BETH CONJUGATE OF X(27) (0.6344, 0.4894) A B C X27 X7 X28 X34 X223 X284 X108 X741 X4 X940 X21 X1214 X1396 (a, b, c) = (5, 6, 7) | AB = 1

X1396 (X27-BETH CONJUGATE OF X27) 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 \(u : v : w\) = X27
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.079817888790\)
▸ Incident Central Lines10 lines

{4, 940}, {7, 27}, {21, 1214}, {28, 34}, {108, 741}, {223, 284}, {269, 1412}, {593, 1014}, {1119, 1407}, {1333, 1427}

▸ Functional Relations2 relations