X3194

X29-CEVA CONJUGATE OF X28

X3194 = X221-cross conjugate of X2360
< 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) { 4, 6 }: Van Aubel Line { 28, 34 }: Central Line L(28, 34) { 29, 81 }: Central Line L(29, 81) { 73, 108 }: Central Line L(73, 108) { 1, 204 }: Central Line L(1, 204) { 196, 221 }: Central Line L(196, 221) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_29 = CEVAPOINT OF INCENTER AND ORTHOCENTER (0.5903, 0.3384) X_28 = CEVAPOINT OF X(19) AND X(25) (0.6285, 0.4382) X_4 = ORTHOCENTER (0.6122, 0.3958) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_73 = CROSSPOINT OF INCENTER AND CIRCUMCENTER (0.5487, 0.1428) X_108 = Ψ(CIRCUMCENTER, INCENTER) (0.5320, 0.6114) X_1 = INCENTER (0.5714, 0.2333) X_204 = -CEVA CONJUGATE OF X(19) (0.6683, 3.3982) X_196 = -CEVA CONJUGATE OF X(4) (0.5649, -0.1989) X_221 = -CEVA CONJUGATE OF X(56) (0.5474, -0.0688) X_3194 = -CEVA CONJUGATE OF X(28) (0.5594, -0.1585) A B C X29 X28 X4 X6 X34 X81 X73 X108 X1 X204 X196 X221 X3194 (a, b, c) = (5, 6, 7) | AB = 1

X3194 (X29-CEVA CONJUGATE OF X28) 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 \(x : y : z\) = X29 and \(u : v : w\) = X28
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): \(0.594148401973\)
▸ Incident Central Lines21 lines

{1, 204}, {4, 6}, {28, 34}, {29, 81}, {40, 2331}, {73, 108}, {112, 972}, {196, 221}, {223, 2360}, {240, 1046}, {329, 3195}, {580, 1715}, {581, 3192}, {937, 1474}, {1104, 1870}, {1193, 1430}, {1203, 1838}, {1741, 1778}, {1828, 2203}, {1875, 2194}, {2266, 2332}

▸ Functional Relations3 relations