X2653

MIDPOINT OF PU(81)

X2653 is the midpoint of pu(81).
< 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) { 661, 2650 }: Central Line L(661, 2650) { 2092, 2183 }: Central Line L(2092, 2183) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_661 = CROSSDIFFERENCE OF X(1) AND X(21) (48.4286, -23.0952) X_2650 = SUM OF PU(81) (0.5919, 0.2602) X_2092 = DANNEELS-APOLLONIUS PERSPECTOR (0.5833, 0.2396) X_2183 = -ISOCONJUGATE OF X(104) (1.5000, 2.4495) X_2653 = MIDPOINT OF PU(81) (0.5918, 0.2602) A B C X661 X2650 X2092 X2183 X2653 (a, b, c) = (5, 6, 7) | AB = 1

X2653 (MIDPOINT OF PU(81)) 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): \(1.124111482848\)
▸ Incident Central Lines2 lines

{661, 2650}, {2092, 2183}