X3127

X4-CEVA CONJUGATE OF X1162

X3127 = X4-Ceva conjugate of X1162
< 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 { 1162, 1165 }: Central Line L(1162, 1165) { 1587, 1899 }: Central Line L(1587, 1899) { 1853, 3070 }: Central Line L(1853, 3070) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_4 = ORTHOCENTER (0.6122, 0.3958) X_1162 = OUTER GREBE-ORTHIC PERSPECTOR (0.6226, 0.4151) X_2 = CENTROID (0.5374, 0.2000) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_1165 = POINT ALTAIS (0.6433, 0.4613) X_1587 = POINT CASTOR I (0.6026, 0.2943) X_1899 = ZOSMA TRANSFORM OF X(1096) (0.6016, 0.1218) X_1853 = ZOSMA TRANSFORM OF X(204) (0.5941, 0.7953) X_3070 = INTERSECTION OF X(4)X(6) AND X(5)X(372) (0.6043, 0.3120) X_3127 = -CEVA CONJUGATE OF X(1162) (0.6030, 0.3716) A B C X4 X1162 X2 X3 X1165 X1587 X1899 X1853 X3070 X3127 (a, b, c) = (5, 6, 7) | AB = 1

X3127 (X4-CEVA CONJUGATE OF X1162) 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 \(x : y : z\) = X4 and \(u : v : w\) = X1162
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): \(41.493551248762\)
▸ Alternate Coordinates1 form

  • Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = (b^{2} + c^{2} + S)/(b^{2} + c^{2} - a^{2}) (E\). Danneels) As a point on the Euler line, X3127 has Shinagawa coefficients \((F,E + F + S)\).

▸ Incident Central Lines4 lines

{2, 3}, {1162, 1165}, {1587, 1899}, {1853, 3070}

▸ Functional Relations1 relation