X2634

MIDPOINT OF PU(75)

X2634 is the midpoint of pu(75).
< 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) { 9, 2629 }: Central Line L(9, 2629) { 2631, 2632 }: Central Line L(2631, 2632) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_9 = MITTENPUNKT (0.5110, 0.1615) X_2629 = CROSSSUM PU(74) (0.8256, -0.9132) X_2631 = SUM OF PU(75) (4.3396, 0.9038) X_2632 = DIFFERENCE OF PU(75) (0.6212, 0.0090) X_2634 = MIDPOINT OF PU(75) (0.5599, -0.0058) A B C X9 X2629 X2631 X2632 X2634 (a, b, c) = (5, 6, 7) | AB = 1

X2634 (MIDPOINT OF PU(75)) 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 \(f(A,B,C) = k(a,b,c)/(\tan C - \tan A) + h(a,b,c)/(\tan B - \tan A)\), where \(h(a,b,c) = a/(\tan C - \tan A) + b/(\tan A - \tan B) + c/(\tan B - \tan C)\), and \(k(a,b,c) = a/(\tan B - \tan A) + b/(\tan C - \tan B) + c/(\tan A - \tan C)\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(3.925900302816\)
▸ Incident Central Lines2 lines

{9, 2629}, {2631, 2632}