X1913

MIDPOINT OF PU(9)

X1913 is the midpoint of pu(9).
< 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) { 213, 667 }: Central Line L(213, 667) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_213 = -CEVA CONJUGATE OF X(42) (0.6135, 0.2833) X_667 = CROSSDIFFERENCE OF X(2) AND X(37) (-6.1667, 5.7155) X_1913 = MIDPOINT OF PU(9) (0.6137, 0.2832) A B C X213 X667 X1913 (a, b, c) = (5, 6, 7) | AB = 1

X1913 (MIDPOINT OF PU(9)) 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 \(f(a,b,c) = a^{2}[2a^{3}bc + ab^{4} + ac^{4} + b^{2}c^{2}(b + c)]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.722504702457\)
▸ Incident Central Lines1 line

{213, 667}