X1032

CYCLOCEVIAN CONJUGATE OF X20

X1032 = isogonal conjugate of X1033
< 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) { 20, 394 }: Central Line L(20, 394) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_4 = ORTHOCENTER (0.6122, 0.3958) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_394 = -CEVA CONJUGATE OF X(3) (0.3778, 0.0284) X_1032 = CYCLOCEVIAN CONJUGATE OF X(20) (0.3836, -0.1007) A B C X4 X69 X20 X394 X1032 (a, b, c) = (5, 6, 7) | AB = 1

X1032 (CYCLOCEVIAN CONJUGATE OF X20) 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 \(f(a,b,c) = 1/[a(w^{2}u^{2} + u^{2}v^{2} - v^{2}w^{2}) + 2uvw(au + bv + cw) \cos A]\), where \(u : v : w\) = X20
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a\),b,c) X3346
Search Value (6, 9, 13): \(3.778893597906\)

X1032 lies on the Lucas cubic.

▸ Incident Central Lines1 line

{20, 394}

▸ Functional Relations5 relations