X3351

X2-CEVA CONJUGATE OF X3342

X3351 = isogonal conjugate of X3352
< 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, 282 }: Central Line L(4, 282) { 57, 1073 }: Central Line L(57, 1073) { 1, 3344 }: Central Line L(1, 3344) { 6, 3342 }: Central Line L(6, 3342) { 9, 3349 }: Central Line L(9, 3349) { 2, 3352 }: Central Line L(2, 3352) 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_3342 = ISOGONAL CONJUGATE OF X(3341) (0.4998, 0.0379) X_4 = ORTHOCENTER (0.6122, 0.3958) X_282 = -CROSS CONJUGATE OF X(9) (0.6199, 0.7507) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_1073 = -CROSS CONJUGATE OF X(3) (0.4792, -0.4343) X_1 = INCENTER (0.5714, 0.2333) X_3344 = ISOGONAL CONJUGATE OF X(3343) (0.5027, 0.1321) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_9 = MITTENPUNKT (0.5110, 0.1615) X_3349 = INTERSECTION OF LINES X(3)X(2130) AND X(4)X(2131) (0.5517, 0.2144) X_3352 = ISOGONAL CONJUGATE OF X(3351) (0.5206, 0.1791) X_3351 = -CEVA CONJUGATE OF X(3342) (0.6100, 0.2900) A B C X2 X3342 X4 X282 X57 X1073 X1 X3344 X6 X9 X3349 X3352 X3351 (a, b, c) = (5, 6, 7) | AB = 1

X3351 (X2-CEVA CONJUGATE OF X3342) 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 \(x : y : z\) = X3342
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(3.002383701974\)

X3351 lies on the Thomson cubic.

▸ Incident Central Lines7 lines

{1, 3344}, {2, 3352}, {4, 282}, {57, 1073}, {6, 3342}, {9, 3349}, {223, 3356}

▸ Functional Relations8 relations