X289

ISOGONAL CONJUGATE OF X236

X289 is the isogonal conjugate of X236.
< 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) { 56, 266 }: Central Line L(56, 266) { 258, 259 }: Central Line L(258, 259) { 1, 363 }: Central Line L(1, 363) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_266 = ISOGONAL CONJUGATE OF X(188) (0.6074, 0.2891) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_258 = CONGRUENT INCIRCLES ISOSCELIZER POINT (0.5464, 0.1945) X_259 = ISOGONAL CONJUGATE OF X(174) (0.5606, 0.2123) X_1 = INCENTER (0.5714, 0.2333) X_363 = EQUAL PERIMETERS ISOSCELIZER POINT (0.5347, 0.2024) X_289 = ISOGONAL CONJUGATE OF X(236) (0.5893, 0.2483) A B C X6 X266 X56 X258 X259 X1 X363 X289 (a, b, c) = (5, 6, 7) | AB = 1

X289 (ISOGONAL CONJUGATE OF X236) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((\sin A/2)/(\cos B/2 + \cos C/2 - \cos A/2) : :\)
Search Value (6, 9, 13): \(1.292903652255\)
▸ Alternate Coordinates2 forms

  • Trilinears: \([1 - \sin(A/2)] \tan(A/2) : :\) (M. Iliev, 4/12/2007)

  • Trilinears: \(a/(1 + \sin(A/2)) : :\)

▸ Incident Central Lines3 lines

{1, 363}, {56, 266}, {258, 259}

▸ Functional Relations3 relations