X3402

TAN(A - ω) POINT

X3402 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) { 42, 263 }: Central Line L(42, 263) { 1, 1755 }: Central Line L(1, 1755) { 1923, 1973 }: Central Line L(1923, 1973) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3403 = COT(A - ω) POINT (0.4262, 0.1032) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_263 = ISOGONAL CONJUGATE OF X(183) (0.6298, 0.3525) X_1 = INCENTER (0.5714, 0.2333) X_1755 = MIMOSA TRANSFORM OF X(287) (1.5943, 2.3982) X_1923 = BICENTRIC SUM OF PU(13) (0.6447, 0.3295) X_1973 = TRILINEAR PRODUCT OF PU(39) (0.6378, 0.4717) X_3402 = TAN(A - ω) POINT (0.6421, 0.3828) A B C X3403 X42 X263 X1 X1755 X1923 X1973 X3402 (a, b, c) = (5, 6, 7) | AB = 1

X3402 (TAN(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 \(f(A,B,C) = \tan(A - \omega )\)
Search Value (6, 9, 13): \(-0.068962181910\)
▸ Alternate Coordinates1 form

  • Trilinears: \(a^{2}/(a^{4} - a^{2} b^{2} - a^{2} c^{2} - 2 b^{2} c^{2}) : :\)

X3402 lies on the cubic K457.

▸ Incident Central Lines3 lines

{1, 1755}, {42, 263}, {1923, 1973}

▸ Functional Relations2 relations