X3341

X2-CEVA CONJUGATE OF X282

X3341 = isogonal conjugate of X3342
< 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) { 4, 57 }: Central Line L(4, 57) { 2, 271 }: Central Line L(2, 271) { 6, 282 }: Central Line L(6, 282) { 1, 1073 }: Central Line L(1, 1073) { 280, 938 }: Central Line L(280, 938) { 9, 3344 }: Central Line L(9, 3344) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_282 = -CROSS CONJUGATE OF X(9) (0.6199, 0.7507) X_4 = ORTHOCENTER (0.6122, 0.3958) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_271 = ISOGONAL CONJUGATE OF X(208) (1.1546, 2.8606) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_1 = INCENTER (0.5714, 0.2333) X_1073 = -CROSS CONJUGATE OF X(3) (0.4792, -0.4343) X_280 = -CROSS CONJUGATE OF X(8) (0.6379, 0.8041) X_938 = ANTICOMPLEMENT OF X(936) (0.5846, 0.2462) X_9 = MITTENPUNKT (0.5110, 0.1615) X_3344 = ISOGONAL CONJUGATE OF X(3343) (0.5027, 0.1321) X_3341 = -CEVA CONJUGATE OF X(282) (0.6101, 0.5135) A B C X2 X282 X4 X57 X271 X6 X1 X1073 X280 X938 X9 X3344 X3341 (a, b, c) = (5, 6, 7) | AB = 1

X3341 (X2-CEVA CONJUGATE OF X282) 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 \(x : y : z\) = X282
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(1.234001162764\)

X3341 lies on the Thomson cubic.

▸ Incident Central Lines8 lines

{1, 1073}, {2, 271}, {3, 3352}, {4, 57}, {6, 282}, {9, 3344}, {223, 3349}, {280, 938}

▸ Functional Relations11 relations