X3356

X6-CROSS CONJUGATE OF X3350

X3356 = X6-cross conjugate of X3350
< 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, 2131 }: Central Line L(3, 2131) { 223, 3351 }: Central Line L(223, 3351) { 1249, 3343 }: Central Line L(1249, 3343) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_3350 = INTERSECTION OF LINES X(3)X(2131) AND X(4)X(1073) (0.5892, 0.2523) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_2131 = ISOGONAL CONJUGATE OF X(2130) (0.5325, 0.1568) X_223 = -CEVA CONJUGATE OF X(57) (0.4996, -0.0528) X_3351 = -CEVA CONJUGATE OF X(3342) (0.6100, 0.2900) X_1249 = ISOGONAL CONJUGATE OF X(1073) (-0.9482, -15.9845) X_3343 = -CEVA CONJUGATE OF X(1073) (0.6143, 0.3503) X_3356 = -CROSS CONJUGATE OF X(3350) (0.6079, 0.2837) A B C X6 X3350 X3 X2131 X223 X3351 X1249 X3343 X3356 (a, b, c) = (5, 6, 7) | AB = 1

X3356 (X6-CROSS CONJUGATE OF X3350) 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 \(f(a,b,c) = u/(-avw + bwu + cuv)\), where \(u : v : w\) = X3350
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(3.803387376288\)

X3356 lies on the Thomson cubic.

▸ Incident Central Lines3 lines

{3, 2131}, {223, 3351}, {1249, 3343}

▸ Functional Relations4 relations