X3019

(SODDY 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) { 1, 7 }: Soddy Line { 6, 13 }: Central Line L(6, 13) 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_7 = GERGONNE POINT (0.5903, 0.2769) 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_3019 = (SODDY LINE)∩(FERMAT AXIS) (0.5909, 0.2783) A B C X1 X7 X6 X13 X3019 (a, b, c) = (5, 6, 7) | AB = 1

X3019 ((SODDY 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 \(f(A,B,C) = \sin(A - C)[1 + 2 \cos(2B)][\sec^{2}(A/2) -\sec^{2}(B/2)] + \sin(A - B)[1 + 2 \cos(2C)][\sec^{2}(A/2) -\sec^{2}(C/2)]\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(0.218215610494\)
▸ Incident Central Lines2 lines

{1, 7}, {6, 13}