X1398

X34-BETH CONJUGATE OF X34

X1398 = isogonal conjugate of X1265
< 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) { 28, 279 }: Central Line L(28, 279) { 184, 221 }: Central Line L(184, 221) { 4, 496 }: Central Line L(4, 496) { 388, 427 }: Central Line L(388, 427) { 1, 1037 }: Central Line L(1, 1037) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_28 = CEVAPOINT OF X(19) AND X(25) (0.6285, 0.4382) X_279 = ISOGONAL CONJUGATE OF X(220) (0.6236, 0.3540) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_221 = -CEVA CONJUGATE OF X(56) (0.5474, -0.0688) X_4 = ORTHOCENTER (0.6122, 0.3958) X_496 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(495) (0.5843, 0.2201) X_388 = ∩X(7)X(8) (0.5790, 0.2635) X_427 = COMPLEMENT OF X(22) (0.5990, 0.3610) X_1 = INCENTER (0.5714, 0.2333) X_1037 = CEVAPOINT OF X(55) AND X(56) (0.5823, 0.2853) X_1398 = -BETH CONJUGATE OF X(34) (0.6338, 0.5315) A B C X34 X25 X28 X279 X184 X221 X4 X496 X388 X427 X1 X1037 X1398 (a, b, c) = (5, 6, 7) | AB = 1

X1398 (X34-BETH CONJUGATE OF X34) 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 \(u : v : w\) = X34
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.006436623356\)
▸ Alternate Coordinates1 form

  • Trilinears: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A, B, C) = \sec A \sin^{4}(A/2)\)

▸ Incident Central Lines15 lines

{1, 1037}, {4, 496}, {6, 1425}, {25, 34}, {28, 279}, {184, 221}, {278, 961}, {388, 427}, {475, 956}, {604, 608}, {607, 1475}, {1106, 1395}, {1254, 1460}, {1394, 1473}, {1407, 1408}

▸ Functional Relations5 relations