X3129

X13-CEVA CONJUGATE OF X6

X3129 = isogonal conjugate of X2992
< 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) { 2, 3 }: Euler Line { 51, 62 }: Central Line L(51, 62) { 61, 184 }: Central Line L(61, 184) { 15, 1495 }: Central Line L(15, 1495) { 13, 1605 }: Central Line L(13, 1605) { 1251, 1953 }: Central Line L(1251, 1953) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_13 = 1st ISOGONIC CENTER (FERMAT POINT, TORRICELLI POINT) (0.5879, 0.2819) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_2 = CENTROID (0.5374, 0.2000) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_51 = CENTROID OF ORTHIC TRIANGLE (0.6093, 0.3186) X_62 = ISOGONAL CONJUGATE OF X(18) (0.6446, 0.3409) X_61 = ISOGONAL CONJUGATE OF X(17) (0.5764, 0.2283) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_15 = 1st ISODYNAMIC POINT (0.5519, 0.1878) X_1495 = CROSSSUM OF X(2) AND X(30) (0.8194, 1.4855) X_1605 = TCC-PERSPECTOR OF X(13) (0.5477, 0.3253) X_1251 = ISOGONAL CONJUGATE OF X(1082) (0.5908, 0.2784) X_1953 = BICENTRIC SUM OF PU(21) (0.5856, 0.2841) X_3129 = -CEVA CONJUGATE OF X(6) (0.5743, 0.2966) A B C X13 X6 X2 X3 X51 X62 X61 X184 X15 X1495 X1605 X1251 X1953 X3129 (a, b, c) = (5, 6, 7) | AB = 1

X3129 (X13-CEVA CONJUGATE OF X6) 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 \(u : v : w\) = X6
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): \(0.387958331762\)
▸ Incident Central Lines8 lines

{2, 3}, {6, 3458}, {13, 1605}, {15, 1495}, {51, 62}, {61, 184}, {619, 2926}, {1251, 1953}

▸ Functional Relations5 relations

Notes

As a point on the Euler line, X3129 has Shinagawa coefficients \((3^{1/2}F - S, -3^{1/2}E - 3^{1/2}F + S)\).