X3404

TAN(A + ω) POINT

X3404 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, 163 }: Central Line L(1, 163) { 63, 561 }: Central Line L(63, 561) { 2157, 2624 }: Central Line L(2157, 2624) { 3401, 3405 }: Central Line L(3401, 3405) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_2236 = -ISOCONJUGATE OF X(733) (2.2504, 2.0410) X_1 = INCENTER (0.5714, 0.2333) X_163 = TRILINEAR PRODUCT X(6)*X(110) (0.3174, 0.5883) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_561 = ISOGONAL CONJUGATE OF 4th POWER POINT (0.4126, 0.1125) X_2157 = -ISOCONJUGATE OF X(23) (0.8254, -0.2862) X_2624 = SUM OF PU(73) (2.8696, 1.7039) X_3401 = COT(A - 2ω) POINT (1.0448, 0.0267) X_3405 = COT(A + ω) POINT (62.1178, 99.9665) X_3404 = TAN(A + ω) POINT (0.8949, -0.2186) A B C X38 X2236 X1 X163 X63 X561 X2157 X2624 X3401 X3405 X3404 (a, b, c) = (5, 6, 7) | AB = 1

X3404 (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 \(f(A,B,C) = \tan(A + \omega )\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(6.564258625425\)

X3404 lies on the cubic K457.

▸ Incident Central Lines4 lines

{1, 163}, {63, 561}, {2157, 2624}, {3401, 3405}

▸ Functional Relations4 relations