X3017

(NAGEL LINE)∩(FERMAT AXIS)

X3017 = X58-of-orthocentroidal triangle
< 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, 2 }: Nagel Line { 6, 13 }: Central Line L(6, 13) { 30, 58 }: Central Line L(30, 58) { 12, 1126 }: Central Line L(12, 1126) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_2 = CENTROID (0.5374, 0.2000) 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_30 = EULER INFINITY POINT (0.7469, 0.7481) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_1126 = ISOGONAL CONJUGATE OF X(1125) (0.5938, 0.2586) X_3017 = (NAGEL LINE)∩(FERMAT AXIS) (0.6027, 0.2639) A B C X1 X2 X6 X13 X30 X58 X12 X1126 X3017 (a, b, c) = (5, 6, 7) | AB = 1

X3017 ((NAGEL 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 \(f(A,B,C) = (\csc A - \csc C) \sin(A - B)[1 + 2 \cos(2C)] - (\csc A - \csc B) \sin(A - C)[1 + 2 \cos(2B)]\)
Search Value (6, 9, 13): \(1.097654959344\)
▸ Incident Central Lines4 lines

{1, 2}, {6, 13}, {12, 1126}, {30, 58}

▸ Functional Relations1 relation

  • X3017 = X58-of-orthocentroidal triangle