X3015

(GERGONNE LINE)∩(FERMAT AXIS)

< 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) { 241, 514 }: Central Line L(241, 514) 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_241 = -LINE CONJUGATE OF X(55) (1.1217, 1.2442) X_514 = ISOGONAL CONJUGATE OF X(101) (1.0761, -0.0329) X_3015 = (GERGONNE LINE)∩(FERMAT AXIS) (-0.9319, 2.1319) A B C X6 X13 X241 X514 X3015 (a, b, c) = (5, 6, 7) | AB = 1

X3015 ((GERGONNE 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 \(f(A,B,C) = (1 + \cos B) \sin(A - B)[1 + 2 \cos(2C)] + (1 + \cos C) \sin(A - C)[1 + 2 \cos(2B)]\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(-0.470397113039\)
▸ Incident Central Lines2 lines

{6, 13}, {241, 514}