X3403

COT(A - ω) POINT

X3403 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, 75 }: Central Line L(1, 75) { 63, 561 }: Central Line L(63, 561) { 76, 1423 }: Central Line L(76, 1423) { 9, 1921 }: Central Line L(9, 1921) { 57, 1920 }: Central Line L(57, 1920) { 19, 1969 }: Central Line L(19, 1969) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3402 = TAN(A - ω) POINT (0.6421, 0.3828) X_1 = INCENTER (0.5714, 0.2333) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_561 = ISOGONAL CONJUGATE OF 4th POWER POINT (0.4126, 0.1125) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_1423 = -BETH CONJUGATE OF X(192) (0.6537, 0.3692) X_9 = MITTENPUNKT (0.5110, 0.1615) X_1921 = CROSSDIFFERENCE OF PU(12) (-1.0027, -0.8795) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_1920 = CROSSSUM OF PU(12) (0.4724, 0.1544) X_19 = CLAWSON POINT (0.6246, 0.4244) X_1969 = TRILINEAR PRODUCT OF PU(38) (0.5432, 0.2926) X_3403 = COT(A - ω) POINT (0.4262, 0.1032) A B C X3402 X1 X75 X63 X561 X76 X1423 X9 X1921 X57 X1920 X19 X1969 X3403 (a, b, c) = (5, 6, 7) | AB = 1

X3403 (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 \(f(A,B,C) = \cot(A - \omega )\)
Search Value (6, 9, 13): \(5.702763521220\)
▸ Alternate Coordinates1 form

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

X3403 lies on the cubic K457.

▸ Incident Central Lines7 lines

{1, 75}, {9, 1921}, {19, 1969}, {57, 1920}, {63, 561}, {76, 1423}, {1707, 1965}

▸ Functional Relations2 relations