X3014

(DE LONGCHAMPS LINE)∩(FERMAT AXIS)

X3014 = isotomic conjugate of X35568
< 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) { 6, 13 }: Central Line L(6, 13) { 325, 523 }: Central Line L(325, 523) { 868, 2854 }: Central Line L(868, 2854) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_13 = 1st ISOGONIC CENTER (FERMAT POINT, TORRICELLI POINT) (0.5879, 0.2819) X_325 = -HIRST INVERSE OF X(69) (-0.3370, -0.7398) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_868 = CROSSPOINT OF X(98) AND X(523) (0.3751, -0.2247) X_2854 = ISOGONAL CONJUGATE OF X(2770) (0.9944, -0.1682) X_3014 = (DE LONGCHAMPS LINE)∩(FERMAT AXIS) (2.2348, -1.7227) A B C X6 X13 X325 X523 X868 X2854 X3014 (a, b, c) = (5, 6, 7) | AB = 1

X3014 ((DE LONGCHAMPS LINE)∩(FERMAT AXIS)) 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 \(f(A,B,C) = \sin^{3} B \sin(A - B)[1 + 2 \cos(2C)] + \sin^{3} C \sin(A - C)[1 + 2 \cos(2B)]\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(3.978406626664\)
▸ Incident Central Lines3 lines

{6, 13}, {325, 523}, {868, 2854}

▸ Functional Relations1 relation

  • X3014 = isotomic conjugate of X35568