X3409

COT(A + 2ω) POINT

X3409 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) { 1, 1917 }: Central Line L(1, 1917) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3408 = TAN(A + 2ω) POINT (0.3833, 0.0893) X_1 = INCENTER (0.5714, 0.2333) X_1917 = TRILINEAR 6th POWER POINT (0.6636, 0.4181) X_3409 = COT(A + 2ω) POINT (0.6532, 0.3973) A B C X3408 X1 X1917 X3409 (a, b, c) = (5, 6, 7) | AB = 1

X3409 (COT(A + 2ω) 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 \(f(A,B,C) = \cot(A + 2\omega )\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(-1.194716357716\)

X3409 lies on the cubic K457.

▸ Incident Central Lines1 line

{1, 1917}

▸ Functional Relations1 relation