X3140

X105-CEVA CONJUGATE OF X523

X3140 = X105-Ceva conjugate of X523
< 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 { 11, 115 }: Central Line L(11, 115) { 125, 2775 }: Central Line L(125, 2775) { 339, 2969 }: Central Line L(339, 2969) { 2968, 2971 }: Central Line L(2968, 2971) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_105 = Λ(INCENTER, SYMMEDIAN POINT) (0.9714, -0.0933) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_2 = CENTROID (0.5374, 0.2000) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_115 = CENTER OF KIEPERT HYPERBOLA (0.7507, 0.0838) X_125 = CENTER OF JERABEK HYPERBOLA (0.6803, 0.0260) X_2775 = ISOGONAL CONJUGATE OF X(2691) (0.9278, 0.6382) X_339 = ISOTOMIC CONJUGATE OF X(250) (0.6002, 0.0170) X_2969 = 3rd MACBEATH POINT (0.7614, 0.2435) X_2968 = 2nd MACBEATH POINT (0.5881, 0.0121) X_2971 = 5th MACBEATH POINT (0.7640, 0.2670) X_3140 = -CEVA CONJUGATE OF X(523) (0.3136, -0.3857) A B C X105 X523 X2 X3 X11 X115 X125 X2775 X339 X2969 X2968 X2971 X3140 (a, b, c) = (5, 6, 7) | AB = 1

X3140 (X105-CEVA CONJUGATE OF X523) 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 \(x : y : z\) = X105 and \(u : v : w\) = X523
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): \(4.197495474869\)
▸ Incident Central Lines5 lines

{2, 3}, {11, 115}, {125, 2775}, {339, 2969}, {2968, 2971}

▸ Functional Relations2 relations

Notes

As a point on the Euler line, X3140 has Shinagawa coefficients \((\$abS_{C}^{3}\$+\$abS_{A}S_{B}\$(E+F) -\$abS_{C}\$[(E+F)^{2}-2S^{2}]-\$ab\$FS^{2}, 3\$abS_{C}\$S^{2}-\$ab\$(E+F)S^{2})\).