X3353

X20-CEVA CONJUGATE OF X84

X3353 = reflection of X3347 in X3
< 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) { 3347, 3 }: Central Line L(3347, 3) { 64, 84 }: Central Line L(64, 84) { 4, 282 }: Central Line L(4, 282) { 1, 3346 }: Central Line L(1, 3346) { 40, 3348 }: Central Line L(40, 3348) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3347 = ISOGONAL CONJUGATE OF X(3182) (0.3848, -0.3283) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_64 = ISOGONAL CONJUGATE OF X(20) (0.5579, 1.5943) X_84 = ISOGONAL CONJUGATE OF X(40) (0.6071, 0.6816) X_4 = ORTHOCENTER (0.6122, 0.3958) X_282 = -CROSS CONJUGATE OF X(9) (0.6199, 0.7507) X_1 = INCENTER (0.5714, 0.2333) X_3346 = ISOGONAL CONJUGATE OF X(1498) (0.4165, -0.8255) X_40 = BEVAN POINT (0.4286, -0.0292) X_3348 = ISOGONAL CONJUGATE OF X(3183) (0.4000, -0.1150) X_3353 = -CEVA CONJUGATE OF X(84) (0.6152, 0.5324) A B C X3347 X3 X64 X84 X4 X282 X1 X3346 X40 X3348 X3353 (a, b, c) = (5, 6, 7) | AB = 1

X3353 (X20-CEVA CONJUGATE OF X84) 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 \(f(a,b,c) = x(84)/(-x(84)/x(20) + y(84)/y(20) + z(84)/z(20))\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(8.801784443289\)

X3353 lies on the Darboux cubic.

▸ Incident Central Lines8 lines

{1, 3346}, {3, 3347}, {4, 282}, {20, 3354}, {40, 3348}, {64, 84}, {1490, 2131}, {1498, 3473}

▸ Functional Relations3 relations