X3401

COT(A - 2ω) POINT

X3401 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, 1581 }: Central Line L(1, 1581) { 63, 1934 }: Central Line L(63, 1934) { 3404, 3405 }: Central Line L(3404, 3405) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3400 = TAN(A - 2ω) POINT (0.9676, 0.9007) X_1 = INCENTER (0.5714, 0.2333) X_1581 = ISOGONAL CONJUGATE OF X(1580) (1.0304, 0.0330) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_1934 = TRILINEAR POLE OF PU(14) (1.0612, 0.0252) X_3404 = TAN(A + ω) POINT (0.8949, -0.2186) X_3405 = COT(A + ω) POINT (62.1178, 99.9665) X_3401 = COT(A - 2ω) POINT (1.0448, 0.0267) A B C X3400 X1 X1581 X63 X1934 X3404 X3405 X3401 (a, b, c) = (5, 6, 7) | AB = 1

X3401 (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): \(-0.306870569836\)

X3401 lies on the cubic K457.

▸ Incident Central Lines3 lines

{1, 1581}, {63, 1934}, {3404, 3405}

▸ Functional Relations1 relation