X2641

MIDPOINT OF PU(78)

X2641 is the midpoint of pu(78).
< 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) { 44, 513 }: Central Line L(44, 513) { 1914, 2651 }: Central Line L(1914, 2651) { 1931, 2642 }: Central Line L(1931, 2642) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_1914 = CROSSDIFFERENCE OF PU(10) (1.1181, 1.0304) X_2651 = CROSSDIFFERENCE OF PU(81) (6.8757, 8.5193) X_1931 = CROSSDIFFERENCE OF PU(32) (1.7418, 1.7715) X_2642 = SUM OF PU(79) (2.3576, 1.9826) X_2641 = MIDPOINT OF PU(78) (1.9999, 2.1774) A B C X44 X513 X1914 X2651 X1931 X2642 X2641 (a, b, c) = (5, 6, 7) | AB = 1

X2641 (MIDPOINT OF PU(78)) 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 \(f(A,B,C) = k(a,b,c)(\cot C - \cot A) + h(a,b,c)(\cot B - \cot A)\), where \(h(a,b,c) = a(\cot C - \cot A) + b(\cot A - \cot B) + c(\cot B - \cot C)\), and \(k(a,b,c) = a(\cot B - \cot A) + b(\cot C - \cot B) + c(\cot A - \cot C)\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(-5.787428016285\)
▸ Incident Central Lines3 lines

{44, 513}, {1914, 2651}, {1931, 2642}