X3408

TAN(A + 2ω) POINT

X3408 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) { 63, 1934 }: Central Line L(63, 1934) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3409 = COT(A + 2ω) POINT (0.6532, 0.3973) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_1934 = TRILINEAR POLE OF PU(14) (1.0612, 0.0252) X_3408 = TAN(A + 2ω) POINT (0.3833, 0.0893) A B C X3409 X63 X1934 X3408 (a, b, c) = (5, 6, 7) | AB = 1

X3408 (TAN(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 \(f(A,B,C) = \tan(A + 2\omega )\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(2.322400741028\)

X3408 lies on the cubic K457.

▸ Incident Central Lines1 line

{63, 1934}

▸ Functional Relations1 relation