X1671

INVERSE-IN-BROCARD-CIRCLE OF X1343

X1671 is the internal center of similitude of the Gallatly circle and the 2nd Lemoine circle. (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) { 1670, 3 }: Brocard Axis { 3, 6 }: Brocard Axis { 76, 1676 }: Central Line L(76, 1676) { 262, 1677 }: Central Line L(262, 1677) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1670 = INVERSE-IN-BROCARD-CIRCLE OF X(1342) (0.4118, -0.0436) 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_1676 = INSIMILICENTER(1st LEMOINE CIRCLE, NINE-POINT CIRCLE) (0.5533, 0.2188) X_262 = ISOGONAL CONJUGATE OF X(182) (0.5893, 0.2856) X_1677 = EXSIMILICENTER(1st LEMOINE CIRCLE, NINE-POINT CIRCLE) (0.6019, 0.7290) X_1671 = INVERSE-IN-BROCARD-CIRCLE OF X(1343) (0.5882, 0.2477) A B C X1670 X3 X6 X76 X1676 X262 X1677 X1671 (a, b, c) = (5, 6, 7) | AB = 1

X1671 (INVERSE-IN-BROCARD-CIRCLE OF X1343) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(\sin A + \cos A \tan(\omega /2) : :\)
Search Value (6, 9, 13): \(1.286118983784\)
▸ Alternate Coordinates6 forms

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

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

  • Trilinears: \(\sin(A + \omega /2) : :\)

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

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

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

▸ Incident Central Lines11 lines

{3, 6}, {76, 1676}, {262, 1677}, {485, 2010}, {486, 2009}, {1124, 2008}, {1335, 2007}, {1377, 2014}, {1378, 2013}, {1702, 2018}, {1703, 2017}

▸ Functional Relations11 relations