X769

o-(- 4, - 3) CIRCUMCIRCLE POINT

1/[\(a^{m-1}(b^{n} - c^{n})\) + \(a^{n-1}(b^{m} - c^{m})\)],

hence the name “(m, n)-circumcircle point”.

< 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) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_768 = ODD (- 4, - 3) INFINITY POINT (-0.0208, 0.3810) X_769 = o-(- 4, - 3) CIRCUMCIRCLE POINT (0.2987, 0.5710) A B C X768 X769 (a, b, c) = (5, 6, 7) | AB = 1

X769 (o-(- 4, - 3) CIRCUMCIRCLE POINT) 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 \(f(a,b,c) = 1/[a ^{-5}(b ^{-3} - c ^{-3}) + a ^{-4}(b ^{-4} - c ^{-4})]\)
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): \(0.558566389944\)

X769 lies on the circumcircle. This is one of several points of the form given by first trilinear

▸ Functional Relations2 relations