X1853

ZOSMA TRANSFORM OF X204

Let A' be the orthocenter of BCX3, and define B' and C' cyclically; then X1853 is the centroid of A'B'C'.
< 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) { 154, 2 }: Central Line L(154, 2) { 4, 64 }: Central Line L(4, 64) { 6, 66 }: Central Line L(6, 66) { 25, 125 }: Central Line L(25, 125) { 3, 161 }: Central Line L(3, 161) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_154 = -CEVA CONJUGATE OF X(6) (0.4807, -0.3954) X_2 = CENTROID (0.5374, 0.2000) X_4 = ORTHOCENTER (0.6122, 0.3958) X_64 = ISOGONAL CONJUGATE OF X(20) (0.5579, 1.5943) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_66 = ISOGONAL CONJUGATE OF X(22) (0.5912, 1.0593) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_125 = CENTER OF JERABEK HYPERBOLA (0.6803, 0.0260) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_161 = -OF-TANGENTIAL-TRIANGLE (0.2845, -1.4852) X_1853 = ZOSMA TRANSFORM OF X(204) (0.5941, 0.7953) A B C X154 X2 X4 X64 X6 X66 X25 X125 X3 X161 X1853 (a, b, c) = (5, 6, 7) | AB = 1

X1853 (ZOSMA TRANSFORM OF X204) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: (y + z) sec A : (z + x) sec B : (x + y) sec C,\(x : y : z\) = X204
Barycentrics: (y + z) tan A : (z + x) tan B : (x + y) tan C,\(x : y : z\) = X204
Search Value (6, 9, 13): \(6.758028414729\)
▸ Incident Central Lines16 lines

{2, 154}, {3, 161}, {4, 64}, {5, 1498}, {6, 66}, {12, 221}, {25, 125}, {122, 1073}, {157, 426}, {343, 1350}, {394, 858}, {1146, 1851}, {1181, 1594}, {1352, 1368}, {1826, 1836}, {1837, 1854}

▸ Functional Relations6 relations