X2649

MIDPOINT OF PU(80)

X2649 is the midpoint of pu(80).
< 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) { 650, 2646 }: Central Line L(650, 2646) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_650 = CROSSDIFFERENCE OF X(1) AND X(3) (13.7143, -4.1991) X_2646 = SUM OF PU(80) (0.5544, 0.2019) X_2649 = MIDPOINT OF PU(80) (0.5540, 0.2021) A B C X650 X2646 X2649 (a, b, c) = (5, 6, 7) | AB = 1

X2649 (MIDPOINT OF PU(80)) 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 \(f(A,B,C) = k(a,b,c)(\cos C + \cos A) + h(a,b,c)(\cos B + \cos A)\), where \(h(a,b,c) = a(\cos C + \cos A) + b(\cos A + \cos B) + c(\cos B + \cos C)\), and \(k(a,b,c) = a(\cos B + \cos A) + b(\cos C + \cos B) + c(\cos A + \cos C)\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(2.627047183843\)
▸ Incident Central Lines1 line

{650, 2646}