X3139

X104-CEVA CONJUGATE OF X523

X3139 = X104-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, 125 }: Central Line L(11, 125) { 123, 136 }: Central Line L(123, 136) { 2968, 2970 }: Central Line L(2968, 2970) { 2969, 2972 }: Central Line L(2969, 2972) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_104 = ANTIPODE OF X(100) (0.8571, -0.2624) 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_125 = CENTER OF JERABEK HYPERBOLA (0.6803, 0.0260) X_123 = -OF-MEDIAL-TRIANGLE (0.5401, -0.0057) X_136 = INTERSECTION OF LINE X(4)X(110) AND X(25)X(132) (0.8024, 0.3155) X_2968 = 2nd MACBEATH POINT (0.5881, 0.0121) X_2970 = 4th MACBEATH POINT (0.7397, 0.1669) X_2969 = 3rd MACBEATH POINT (0.7614, 0.2435) X_2972 = 6th MACBEATH POINT (0.5552, 0.0030) X_3139 = -CEVA CONJUGATE OF X(523) (0.3872, -0.1930) A B C X104 X523 X2 X3 X11 X125 X123 X136 X2968 X2970 X2969 X2972 X3139 (a, b, c) = (5, 6, 7) | AB = 1

X3139 (X104-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 \(x : y : z\) = X104 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): \(3.838825550424\)
▸ Incident Central Lines5 lines

{2, 3}, {11, 125}, {123, 136}, {2968, 2970}, {2969, 2972}

▸ Functional Relations1 relation

Notes

As a point on the Euler line, X3139 has Shinagawa coefficients \((2\$aS_{B}S_{C}\$+3\$aS_{A}\$F-\$a\$S^{2}, \$aS_{A}\$(E+F)-\$a\$S^{2})\).