X3181

X14-CEVA CONJUGATE OF X2

X3181 = anticomplement of X299
< A B C >: Reference Triangle △ABC < K_a K_b K_c >: Anticomplementary Triangle △K_a K_b K_c [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 2, 299 }: Centroid–Symmedian Line { 2, 6 }: Centroid–Symmedian Line { 14, 532 }: Central Line L(14, 532) { 16, 533 }: Central Line L(16, 533) { 148, 530 }: Central Line L(148, 530) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) K_a = Anticomplementary Vertex K_a (1.6122, 0.5999) K_b = Anticomplementary Vertex K_b (-0.3878, 0.5999) K_c = Anticomplementary Vertex K_c (0.3878, -0.5999) X_2 = CENTROID (0.5374, 0.2000) X_299 = ISOTOMIC CONJUGATE OF 2nd ISOGONIC CENTER (-1.1465, -1.6097) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_14 = 2nd ISOGONIC CENTER (0.9134, -0.1143) X_532 = DIRECTION OF VECTOR AX + BX + CX, where X = X(17) (0.8927, 0.6671) X_16 = 2nd ISODYNAMIC POINT (1.8453, 2.3239) X_533 = DIRECTION OF VECTOR AX + BX + CX, where X = X(18) (0.0625, -0.1448) X_148 = STEINER POINT OF ANTICOMPLEMENTARY TRIANGLE (1.3904, -0.2646) X_530 = DIRECTION OF VECTOR AX + BX + CX, where X = X(13) (0.8451, 0.6997) X_3181 = -CEVA CONJUGATE OF X(2) (3.9052, 3.8193) A B C Ka Kb Kc X2 X299 X6 X14 X532 X16 X533 X148 X530 X3181 (a, b, c) = (5, 6, 7) | AB = 1

X3181 (X14-CEVA CONJUGATE OF X2) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(u(-u/x + v/y + w/z) : v(u/x - v/y + w/z) : w(u/x + v/y - w/z)\), where \(x : y : z\) = X14 and \(u : v : w\) = X2
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\), where \(f(a,b,c) = u(-u/x + v/y + w/z)\)
Search Value (6, 9, 13): \(-12.709665825117\)
▸ Incident Central Lines8 lines

{2, 6}, {14, 532}, {16, 533}, {61, 618}, {62, 633}, {148, 530}, {194, 616}, {1080, 1351}

▸ Functional Relations6 relations