X1690

INVERSE-IN-BROCARD-CIRCLE OF X1688

X1690 is the internal center of similitude of the Gallatly circle and the circumcircle. (Peter J. C. Moses, 9/03)
< 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) { 1689, 6 }: Brocard Axis { 3, 6 }: Brocard Axis A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1689 = INVERSE-IN-BROCARD-CIRCLE OF X(1687) (0.6471, 0.3451) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_1690 = INVERSE-IN-BROCARD-CIRCLE OF X(1688) (0.5529, 0.1894) A B C X1689 X6 X3 X1690 (a, b, c) = (5, 6, 7) | AB = 1

X1690 (INVERSE-IN-BROCARD-CIRCLE OF X1688) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(\cos(A + \omega /2 - \pi /4) : \cos(B + \omega /2 - \pi /4) : \cos(C + \omega /2 - \pi /4)\)
Search Value (6, 9, 13): \(2.811997584933\)
▸ Alternate Coordinates4 forms

  • Trilinears: \(\sin(A + \omega /2 + \pi /4) : \sin(B + \omega /2 + \pi /4) : \sin(C + \omega /2 + \pi /4)\)

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

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

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

▸ Incident Central Lines11 lines

{1, 2017}, {2, 2010}, {3, 6}, {4, 2009}, {55, 2008}, {56, 2007}, {165, 2018}, {958, 2014}, {1344, 2016}, {1345, 2015}, {1376, 2013}

▸ Functional Relations5 relations