X3343

X2-CEVA CONJUGATE OF X1073

X3343 = isogonal conjugate of X3344
< A B C >: Reference Triangle △ABC < M_a M_b M_c >: Medial Triangle △M_a M_b M_c [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 2, 1032 }: Central Line L(2, 1032) { 4, 64 }: Central Line L(4, 64) { 57, 282 }: Central Line L(57, 282) { 6, 1073 }: Central Line L(6, 1073) { 154, 1301 }: Central Line L(154, 1301) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) M_a = Midpoint M_a of BC (0.8061, 0.2999) M_b = Midpoint M_b of CA (0.3061, 0.2999) M_c = Midpoint M_c of AB (0.5000, 0.0000) X_2 = CENTROID (0.5374, 0.2000) X_1032 = CYCLOCEVIAN CONJUGATE OF X(20) (0.3836, -0.1007) X_4 = ORTHOCENTER (0.6122, 0.3958) X_64 = ISOGONAL CONJUGATE OF X(20) (0.5579, 1.5943) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_282 = -CROSS CONJUGATE OF X(9) (0.6199, 0.7507) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_1073 = -CROSS CONJUGATE OF X(3) (0.4792, -0.4343) X_154 = -CEVA CONJUGATE OF X(6) (0.4807, -0.3954) X_1301 = COLLINGS TRANSFORM OF X(235) (0.6568, 0.5877) X_3343 = -CEVA CONJUGATE OF X(1073) (0.6143, 0.3503) A B C Ma Mb Mc X2 X1032 X4 X64 X57 X282 X6 X1073 X154 X1301 X3343 (a, b, c) = (5, 6, 7) | AB = 1

X3343 (X2-CEVA CONJUGATE OF X1073) 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 \(f(a,b,c) = x(-ax + by + cz)\), where \(x : y : z\) = X1073
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(2.054606389780\)

X3343 lies on the Thomson cubic.

▸ Incident Central Lines9 lines

{1, 3342}, {2, 1032}, {3, 2130}, {4, 64}, {6, 1073}, {9, 3352}, {57, 282}, {154, 1301}, {1249, 3356}

▸ Functional Relations9 relations