X1865

ZOSMA TRANSFORM OF X284

X1865 = X4-Ceva conjugate of X1859
< 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 { 12, 37 }: Central Line L(12, 37) { 19, 407 }: Central Line L(19, 407) { 33, 430 }: Central Line L(33, 430) { 286, 297 }: Central Line L(286, 297) { 281, 860 }: Central Line L(281, 860) 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_1859 = ZOSMA TRANSFORM OF X(226) (0.6113, 0.3833) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_19 = CLAWSON POINT (0.6246, 0.4244) X_407 = CROSSPOINT OF X(4) AND X(225) (0.6211, 0.4189) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_430 = EULER X(81)-5th-SUBSTITUTION POINT (0.6091, 0.3875) X_286 = -CROSS CONJUGATE OF X(27) (0.6033, 0.3810) X_297 = -HIRST INVERSE OF X(4) (0.8440, 1.0022) X_281 = -CROSS CONJUGATE OF X(9) (0.5796, 0.3202) X_860 = INTERCEPT OF EULER LINE AND TRILINEAR POLAR OF X(92) (0.7856, 0.8494) X_1865 = ZOSMA TRANSFORM OF X(284) (0.6133, 0.4068) A B C X4 X1859 X6 X12 X37 X19 X407 X33 X430 X286 X297 X281 X860 X1865 (a, b, c) = (5, 6, 7) | AB = 1

X1865 (ZOSMA TRANSFORM OF X284) 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,\(x : y : z\) = X284
Barycentrics: (y + z) tan A : (z + x) tan B : (x + y) tan C,\(x : y : z\) = X284
Search Value (6, 9, 13): \(-2.494546430321\)
▸ Incident Central Lines10 lines

{4, 6}, {12, 37}, {19, 407}, {33, 430}, {92, 1211}, {209, 1824}, {281, 860}, {286, 297}, {442, 1838}, {1474, 1884}

▸ Functional Relations2 relations