X3375

TAN(A - π/3) POINT

X3375 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) { 17, 1652 }: Central Line L(17, 1652) { 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_1095 = TRILINEAR SQUARE OF X(16) (0.4127, 0.3906) X_1 = INCENTER (0.5714, 0.2333) X_17 = 1st NAPOLEON POINT (0.5666, 0.2383) X_1652 = 4th EVANS PERSPECTOR (0.5899, 0.2763) X_19 = CLAWSON POINT (0.6246, 0.4244) X_2290 = -ISOCONJUGATE OF X(1141) (1.8189, 2.2759) X_3375 = TAN(A - π/3) POINT (1.7620, 2.1876) A B C X1095 X1 X17 X1652 X19 X2290 X3375 (a, b, c) = (5, 6, 7) | AB = 1

X3375 (TAN(A - π/3) 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 \(f(A,B,C) = \tan(A - \pi /3)\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(-2.595788055999\)
▸ Incident Central Lines2 lines

{17, 1652}, {19, 2290}

▸ Functional Relations3 relations