X3468

X5-CEVA CONJUGATE OF X3336

X3468 = isogonal conjugate of X3469
< 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) { 1, 4 }: Incenter–Orthocenter Line { 36, 1410 }: Central Line L(36, 1410) { 62, 1652 }: Central Line L(62, 1652) { 62, 1653 }: Central Line L(62, 1653) { 47, 1758 }: Central Line L(47, 1758) { 1047, 1718 }: Central Line L(1047, 1718) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_3336 = INTERSECTION OF LINES X(1)X(3) AND X(7)X(498) (0.6341, 0.3483) X_1 = INCENTER (0.5714, 0.2333) X_4 = ORTHOCENTER (0.6122, 0.3958) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_1410 = -BETH CONJUGATE OF X(73) (0.6303, 0.2394) X_62 = ISOGONAL CONJUGATE OF X(18) (0.6446, 0.3409) X_1652 = 4th EVANS PERSPECTOR (0.5899, 0.2763) X_1653 = 5th EVANS PERSPECTOR (0.6584, 0.3759) X_47 = -BETH CONJUGATE OF X(34) (0.7279, 0.4389) X_1758 = MIMOSA TRANSFORM OF X(296) (1.1982, 1.3847) X_1047 = -CEVA CONJUGATE OF X(1) (0.5281, -0.0076) X_1718 = MIMOSA TRANSFORM OF X(36) (0.1143, 0.6999) X_3468 = -CEVA CONJUGATE OF X(3336) (0.5161, 0.0130) A B C X5 X3336 X1 X4 X36 X1410 X62 X1652 X1653 X47 X1758 X1047 X1718 X3468 (a, b, c) = (5, 6, 7) | AB = 1

X3468 (X5-CEVA CONJUGATE OF X3336) 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 \(f(a,b,c) = x(- x/u + y/v + z/w)\), where \(u : v : w\) = X5,\(x : y : z\) = X3336
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.050657137784\)
▸ Alternate Coordinates1 form

  • Trilinears: \(2 - \sec A + \sec B + \sec C : :\)

X3468 lies on the Napoleon cubic.

▸ Incident Central Lines13 lines

{1, 4}, {5, 3469}, {36, 1410}, {47, 1758}, {54, 3336}, {62, 1652}, {62, 1653}, {195, 3461}, {610, 2317}, {1047, 1718}, {1051, 2939}, {3460, 3463}, {3467, 3470}

▸ Functional Relations3 relations