X945

ISOGONAL CONJUGATE OF X944

X945 is the isogonal conjugate of X944.
< 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) { 78, 517 }: Central Line L(78, 517) { 283, 859 }: Central Line L(283, 859) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_944 = HOFSTADTER TRAPEZOID POINT (0.5306, 0.0708) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8180, 0.7154) X_283 = -CROSS CONJUGATE OF X(21) (0.4475, 0.0704) X_859 = INTERCEPT OF EULER LINE AND TRILINEAR POLAR OF X(81) (1.1279, 1.7448) X_945 = ISOGONAL CONJUGATE OF X(944) (0.6020, 0.4506) A B C X944 X78 X517 X283 X859 X945 (a, b, c) = (5, 6, 7) | AB = 1

X945 (ISOGONAL CONJUGATE OF X944) 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 \(f(a,b,c) = a/[3a^{4} - 2a^{3}(b + c) + (b - c)^{2}(2ab + 2ac - 2bc - b^{2} - c^{2} - 2a^{2})]\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(-28.107306354614\)
▸ Incident Central Lines2 lines

{78, 517}, {283, 859}

▸ Functional Relations2 relations