X3384

COT(A - π/6) POINT

X3384 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) { 18, 1653 }: Central Line L(18, 1653) { 19, 2290 }: Central Line L(19, 2290) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1094 = TRILINEAR SQUARE OF X(15) (0.5301, 0.1475) X_1 = INCENTER (0.5714, 0.2333) X_18 = 2nd NAPOLEON POINT (0.4434, 0.1317) X_1653 = 5th EVANS PERSPECTOR (0.6584, 0.3759) X_19 = CLAWSON POINT (0.6246, 0.4244) X_2290 = -ISOCONJUGATE OF X(1141) (1.8189, 2.2759) X_3384 = COT(A - π/6) POINT (0.4151, 0.0995) A B C X1094 X1 X18 X1653 X19 X2290 X3384 (a, b, c) = (5, 6, 7) | AB = 1

X3384 (COT(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 \(f(A,B,C) = \cot(A - \pi /6)\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(-30.987829027645\)
▸ Alternate Coordinates1 form

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

▸ Incident Central Lines2 lines

{18, 1653}, {19, 2290}

▸ Functional Relations3 relations