X3103

OUTER VERTEX OF THE BROCARD SQUARE

X3103 is the vertex of the Brocard square that is farest from X3; see X3102.
< 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) { 3102, 39 }: Brocard Axis { 3, 6 }: Brocard Axis { 76, 485 }: Central Line L(76, 485) { 194, 487 }: Central Line L(194, 487) { 262, 486 }: Central Line L(262, 486) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3102 = INNER VERTEX OF THE BROCARD SQUARE (0.5362, 0.1619) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_485 = VECTEN POINT (0.5773, 0.2578) X_194 = -CEVA CONJUGATE OF X(2) (0.6989, 0.3222) X_487 = ANTICOMPLEMENT OF X(486) (1.7742, 0.6338) X_262 = ISOGONAL CONJUGATE OF X(182) (0.5893, 0.2856) X_486 = INNER VECTEN POINT (-0.0810, -0.0170) X_3103 = OUTER VERTEX OF THE BROCARD SQUARE (0.6194, 0.2992) A B C X3102 X39 X3 X6 X76 X485 X194 X487 X262 X486 X3103 (a, b, c) = (5, 6, 7) | AB = 1

X3103 (OUTER VERTEX OF THE BROCARD SQUARE) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(\cos(A + \omega + \pi /4) : :\)
Barycentrics: \(a^{2} (b^{4} + c^{4} - a^{2} b^{2} - a^{2} c^{2} - 2 S (b^{2} + c^{2})) : :\)
Search Value (6, 9, 13): \(-0.162480554516\)
▸ Alternate Coordinates5 forms

  • Trilinears: \(\sin(A + \omega - \pi /4) : :\)

  • Trilinears: \(bc \cos^{2} A - a^{2}\cos B \cos C - ab \sin B - ac \sin C : :\)

  • Trilinears: \(\sin A - \cos(A + 2\omega ) : :\)

  • Trilinears: \(\cos A - \sin(A + 2\omega ) : :\)

  • Trilinears: \(\cos(A + \omega ) - \sin(A + \omega ) : :\)

▸ Incident Central Lines6 lines

{3, 6}, {76, 485}, {194, 487}, {262, 486}, {325, 639}, {2782, 3070}

▸ Functional Relations2 relations