X2657

MIDPOINT OF PU(82)

X2657 is the midpoint of pu(82).
< 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) { 37, 2190 }: Central Line L(37, 2190) { 652, 2654 }: Central Line L(652, 2654) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_2190 = -ISOCONJUGATE OF X(216) (0.6223, 0.3794) X_652 = CROSSDIFFERENCE OF X(1) AND X(4) (7.2558, -0.6836) X_2654 = SUM OF PU(82) (0.5822, 0.2761) X_2657 = MIDPOINT OF PU(82) (0.5810, 0.2763) A B C X37 X2190 X652 X2654 X2657 (a, b, c) = (5, 6, 7) | AB = 1

X2657 (MIDPOINT OF PU(82)) 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 \(f(A,B,C) = k(a,b,c)(\sec C + \sec A) + h(a,b,c)(\sec B + \sec A)\), where \(h(a,b,c) = a(\sec C + \sec A) + b(\sec A + \sec B) + c(\sec B + \sec C)\), and \(k(a,b,c) = a(\sec B + \sec A) + b(\sec C + \sec B) + c(\sec A + \sec C)\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(-14.244422908103\)
▸ Incident Central Lines2 lines

{37, 2190}, {652, 2654}