X1165

POINT ALTAIS

< 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) { 468, 1164 }: Central Line L(468, 1164) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_468 = -LINE CONJUGATE OF X(3) (0.7498, 0.7558) X_1164 = POINT ALTAIR (0.6143, 0.3811) X_1165 = POINT ALTAIS (0.6433, 0.4613) A B C X468 X1164 X1165 (a, b, c) = (5, 6, 7) | AB = 1

X1165 (POINT ALTAIS) 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 \(f(a,b,c) = (\operatorname{area} - a^{2})(2 \operatorname{area} + b^{2} + c^{2})/[a(b^{2} + c^{2} - a^{2})]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.415378360401\)
▸ Incident Central Lines1 line

{468, 1164}