X3383

TAN(A - π/6) POINT

X3383 and related points occupy Bernard Gibert’s Table 38. See the note at X3364.
< 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) { 13, 484 }: Central Line L(13, 484) { 1, 1094 }: Central Line L(1, 1094) { 19, 2166 }: Central Line L(19, 2166) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3384 = COT(A - π/6) POINT (0.4151, 0.0995) X_13 = 1st ISOGONIC CENTER (FERMAT POINT, TORRICELLI POINT) (0.5879, 0.2819) X_484 = 1st EVANS PERSPECTOR (2.0952, 3.0327) X_1 = INCENTER (0.5714, 0.2333) X_1094 = TRILINEAR SQUARE OF X(15) (0.5301, 0.1475) X_19 = CLAWSON POINT (0.6246, 0.4244) X_2166 = -ISOCONJUGATE OF X(50) (0.9476, -0.1665) X_3383 = TAN(A - π/6) POINT (0.6453, 0.3866) A B C X3384 X13 X484 X1 X1094 X19 X2166 X3383 (a, b, c) = (5, 6, 7) | AB = 1

X3383 (TAN(A - π/6) POINT) 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 \(f(A,B,C) = \tan(A - \pi /6)\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(-0.008317186017\)
▸ Alternate Coordinates1 form

  • Trilinears: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A,B,C) = \cot(A + \pi /3)\)

▸ Incident Central Lines3 lines

{1, 1094}, {13, 484}, {19, 2166}

▸ Functional Relations2 relations