X1050

POINT ALGOL

< 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) { 1, 341 }: Central Line L(1, 341) { 40, 978 }: Central Line L(40, 978) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_341 = ISOTOMIC CONJUGATE OF X(269) (0.3509, 0.0650) X_40 = BEVAN POINT (0.4286, -0.0292) X_978 = -CEVA CONJUGATE OF X(1) (0.7456, 0.4040) X_1050 = POINT ALGOL (0.6830, 0.3184) A B C X1 X341 X40 X978 X1050 (a, b, c) = (5, 6, 7) | AB = 1

X1050 (POINT ALGOL) 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 \(f(a,b,c) = -u^{2} + v^{2} + w^{2} + vw + wu + uv\),\(u : v : w\) = X8
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): \(-0.484759620081\)
▸ Incident Central Lines2 lines

{1, 341}, {40, 978}