X3180

X13-CEVA CONJUGATE OF X2

X3180 = anticomplement of X298
< 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, 298 }: Centroid–Symmedian Line { 2, 6 }: Centroid–Symmedian Line { 13, 533 }: Central Line L(13, 533) { 148, 531 }: Central Line L(148, 531) { 62, 619 }: Central Line L(62, 619) 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_298 = ISOTOMIC CONJUGATE OF 1st ISOGONIC CENTER (0.4724, 0.1301) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_13 = 1st ISOGONIC CENTER (FERMAT POINT, TORRICELLI POINT) (0.5879, 0.2819) 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_531 = DIRECTION OF VECTOR AX + BX + CX, where X = X(14) (0.9877, -0.1764) X_62 = ISOGONAL CONJUGATE OF X(18) (0.6446, 0.3409) X_619 = COMPLEMENT OF X(14) (0.3494, 0.3571) X_3180 = -CEVA CONJUGATE OF X(2) (0.6674, 0.3397) A B C Ka Kb Kc X2 X298 X6 X13 X533 X148 X531 X62 X619 X3180 (a, b, c) = (5, 6, 7) | AB = 1

X3180 (X13-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 \(x : y : z\) = X13 and \(u : v : w\) = X2
Search Value (6, 9, 13): \(-1.531328032547\)
▸ Incident Central Lines7 lines

{2, 6}, {13, 533}, {61, 634}, {62, 619}, {148, 531}, {194, 617}, {383, 1351}

▸ Functional Relations6 relations