X242

X4-LINE CONJUGATE OF X71

X242 = X4-Hirst inverse of X19
< 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) { 4, 9 }: Orthocenter–Spieker Line { 25, 92 }: Central Line L(25, 92) { 34, 87 }: Central Line L(34, 87) { 29, 257 }: Central Line L(29, 257) { 28, 261 }: Central Line L(28, 261) { 162, 422 }: Central Line L(162, 422) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_4 = ORTHOCENTER (0.6122, 0.3958) X_71 = ISOGONAL CONJUGATE OF X(27) (0.4807, 0.0915) X_9 = MITTENPUNKT (0.5110, 0.1615) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_92 = CEVAPOINT OF INCENTER AND CLAWSON POINT (0.5949, 0.3639) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_87 = -CROSS CONJUGATE OF X(1) (0.4794, 0.1691) X_29 = CEVAPOINT OF INCENTER AND ORTHOCENTER (0.5903, 0.3384) X_257 = ISOGONAL CONJUGATE OF X(172) (0.5240, 0.1822) X_28 = CEVAPOINT OF X(19) AND X(25) (0.6285, 0.4382) X_261 = ISOTOMIC CONJUGATE OF X(12) (0.5072, 0.1625) X_162 = CEVAPOINT OF X(108) AND X(109) (0.4897, 0.6018) X_422 = -HIRST INVERSE OF X(28) (0.7315, 0.7077) X_242 = -LINE CONJUGATE OF X(71) (0.7507, 0.7161) A B C X4 X71 X9 X25 X92 X34 X87 X29 X257 X28 X261 X162 X422 X242 (a, b, c) = (5, 6, 7) | AB = 1

X242 (X4-LINE CONJUGATE OF X71) 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 \(f(A,B,C) = (\sec A)(\sin^{2} A - \sin B \sin C)\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(1.163624376275\)
▸ Incident Central Lines9 lines

{4, 9}, {25, 92}, {28, 261}, {29, 257}, {34, 87}, {162, 422}, {238, 419}, {278, 459}, {915, 929}

▸ Functional Relations8 relations