X3164

X3-CEVA CONJUGATE OF X2

X3164 = reflection of X264 in X216
< 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) { 264, 216 }: Central Line L(264, 216) { 20, 185 }: Central Line L(20, 185) { 2, 216 }: Central Line L(2, 216) { 6, 401 }: Central Line L(6, 401) { 22, 385 }: Central Line L(22, 385) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_264 = ISOTOMIC CONJUGATE OF CIRCUMCENTER (0.5720, 0.3293) X_216 = -CEVA CONJUGATE OF X(51) (0.5201, 0.1353) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_185 = NAGEL POINT OF THE ORTHIC TRIANGLE (0.6033, 0.1643) X_2 = CENTROID (0.5374, 0.2000) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_401 = BAILEY POINT (-0.0758, -1.4044) X_22 = EXETER POINT (0.4143, -0.1221) X_385 = -HIRST INVERSE OF X(6) (2.2863, 2.0795) X_3164 = -CEVA CONJUGATE OF X(2) (0.4683, -0.0587) A B C X264 X216 X20 X185 X2 X6 X401 X22 X385 X3164 (a, b, c) = (5, 6, 7) | AB = 1

X3164 (X3-CEVA CONJUGATE OF X2) 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 \(x : y : z\) = X3 and \(u : v : w\) = X2
Barycentrics: \(\csc 2A - \csc 2B - \csc 2C : \csc 2B - \csc 2C - \csc 2A : \csc 2C - \csc 2A - \csc 2B\) (P. Moses, 5/24/07)
Search Value (6, 9, 13): \(-9.830507424580\)
▸ Incident Central Lines11 lines

{2, 216}, {6, 401}, {20, 185}, {22, 385}, {69, 1972}, {160, 523}, {206, 1632}, {237, 3186}, {577, 648}, {1976, 2998}, {3101, 3187}

▸ Functional Relations11 relations