X3405

COT(A + ω) POINT

X3405 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, 82 }: Central Line L(1, 82) { 798, 812 }: Central Line L(798, 812) { 19, 1969 }: Central Line L(19, 1969) { 3401, 3404 }: Central Line L(3401, 3404) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1755 = MIMOSA TRANSFORM OF X(287) (1.5943, 2.3982) X_1959 = CROSSDIFFERENCE OF PU(23) (-0.9410, -1.7546) X_1 = INCENTER (0.5714, 0.2333) X_82 = ISOGONAL CONJUGATE OF X(38) (0.5943, 0.2703) X_798 = CROSSDIFFERENCE OF X(1) AND X(75) (-13.4299, 10.5763) X_812 = ODD (- 1, 1) INFINITY POINT (0.1586, -0.2483) X_19 = CLAWSON POINT (0.6246, 0.4244) X_1969 = TRILINEAR PRODUCT OF PU(38) (0.5432, 0.2926) X_3401 = COT(A - 2ω) POINT (1.0448, 0.0267) X_3404 = TAN(A + ω) POINT (0.8949, -0.2186) X_3405 = COT(A + ω) POINT (62.1178, 99.9665) A B C X1755 X1959 X1 X82 X798 X812 X19 X1969 X3401 X3404 X3405 (a, b, c) = (5, 6, 7) | AB = 1

X3405 (COT(A + ω) 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 \(f(A,B,C) = \cot(A + \omega )\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(-42.899103781415\)
▸ Alternate Coordinates1 form

  • Trilinears: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A,B,C) = \cos(A + 2\pi omega)\)

X3405 lies on the cubic K457.

▸ Incident Central Lines4 lines

{1, 82}, {19, 1969}, {798, 812}, {3401, 3404}

▸ Functional Relations3 relations