X1825

ZOSMA TRANSFORM OF X5

X1825 = isogonal conjugate of X1789
< 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) { 19, 41 }: Central Line L(19, 41) { 33, 40 }: Central Line L(33, 40) { 4, 80 }: Central Line L(4, 80) { 35, 186 }: Central Line L(35, 186) { 65, 225 }: Central Line L(65, 225) { 250, 270 }: Central Line L(250, 270) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1789 = INVERSE MIMOSA TRANSFORM OF X(5) (0.4896, 0.1064) X_19 = CLAWSON POINT (0.6246, 0.4244) X_41 = -CEVA CONJUGATE OF X(31) (0.5823, 0.2244) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_40 = BEVAN POINT (0.4286, -0.0292) X_4 = ORTHOCENTER (0.6122, 0.3958) X_80 = REFLECTION OF INCENTER IN FEUERBACH POINT (0.8980, -0.1000) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_186 = INVERSE-IN-CIRCUMCIRCLE OF X(4) (0.7957, 0.8758) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_225 = -CEVA CONJUGATE OF X(65) (0.6246, 0.4451) X_250 = ISOGONAL CONJUGATE OF X(125) (0.5892, 0.5347) X_270 = ISOGONAL CONJUGATE OF X(201) (0.6168, 0.3881) X_1825 = ZOSMA TRANSFORM OF X(5) (0.6169, 0.3877) A B C X1789 X19 X41 X33 X40 X4 X80 X35 X186 X65 X225 X250 X270 X1825 (a, b, c) = (5, 6, 7) | AB = 1

X1825 (ZOSMA TRANSFORM OF X5) 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,\(x : y : z\) = X5
Barycentrics: (y + z) tan A : (z + x) tan B : (x + y) tan C,\(x : y : z\) = X5
Search Value (6, 9, 13): \(2.730257027834\)
▸ Incident Central Lines13 lines

{4, 80}, {19, 41}, {33, 40}, {34, 1126}, {35, 186}, {65, 225}, {109, 1710}, {250, 270}, {319, 340}, {1829, 1877}, {1859, 1902}, {1872, 1905}, {1875, 1900}

▸ Functional Relations2 relations

  • X1825 = isogonal conjugate of X1789

  • X1825 = polar conjugate of isogonal conjugate of X21741