X1806

INVERSE MIMOSA TRANSFORM OF X372

X1806 = X21-Ceva conjugate of X1805
< 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) { 3, 6 }: Brocard Axis A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_1805 = INVERSE MIMOSA TRANSFORM OF X(371) (0.4959, 0.0953) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_1806 = INVERSE MIMOSA TRANSFORM OF X(372) (0.5819, 0.2373) A B C X21 X1805 X3 X6 X1806 (a, b, c) = (5, 6, 7) | AB = 1

X1806 (INVERSE MIMOSA TRANSFORM OF X372) 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 \(f(a,b,c) = a[1 + \cot(A/2)]/(b + c)\) (M. Iliev, 5/13/07)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(1.674674929180\)
▸ Alternate Coordinates1 form

  • Trilinears: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A,B,C) = \sec[(B - C)/2)][\sin(A/2) + \cos(A/2)]\) (M. Iliev, 5/13/07)

▸ Incident Central Lines1 line

{3, 6}

▸ Functional Relations3 relations