X3135

X96-CEVA CONJUGATE OF X6

X3135 = X96-Ceva conjugate of X6
< 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 { 160, 184 }: Central Line L(160, 184) { 51, 570 }: Central Line L(51, 570) { 161, 2351 }: Central Line L(161, 2351) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_96 = ISOGONAL CONJUGATE OF X(52) (-0.0943, -0.0197) 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_160 = -OF-TANGENTIAL-TRIANGLE (0.4841, -0.0647) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_51 = CENTROID OF ORTHIC TRIANGLE (0.6093, 0.3186) X_570 = ORTHOGONAL OF X(52) (0.5652, 0.2098) X_161 = -OF-TANGENTIAL-TRIANGLE (0.2845, -1.4852) X_2351 = -ISOCONJUGATE OF X(1748) (-0.0825, -0.0111) X_3135 = -CEVA CONJUGATE OF X(6) (0.1302, -0.8655) A B C X96 X6 X2 X3 X160 X184 X51 X570 X161 X2351 X3135 (a, b, c) = (5, 6, 7) | AB = 1

X3135 (X96-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 \(x : y : z\) = X96 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): \(-4.722636646479\)
▸ Incident Central Lines4 lines

{2, 3}, {51, 570}, {160, 184}, {161, 2351}

▸ Functional Relations2 relations

Notes

As a point on the Euler line, X3135 has Shinagawa coefficients \(((E + 2F)F + 2S^{2}, -(E + F)(E + 2F) - 2S^{2})\).