X1289

COLLINGS TRANSFORM OF X25

X1289 = trilinear pole of line X6X66
< 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) { 24, 98 }: Central Line L(24, 98) { 4, 127 }: Central Line L(4, 127) { 66, 74 }: Central Line L(66, 74) { 25, 339 }: Central Line L(25, 339) { 111, 459 }: Central Line L(111, 459) { 403, 842 }: Central Line L(403, 842) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_24 = PERSPECTOR OF ABC AND ORTHIC-OF-ORTHIC TRIANGLE (0.6627, 0.5278) X_98 = TARRY POINT (0.8891, -0.2281) X_4 = ORTHOCENTER (0.6122, 0.3958) X_127 = -OF-MEDIAL-TRIANGLE (0.5480, -0.0061) X_66 = ISOGONAL CONJUGATE OF X(22) (0.5912, 1.0593) X_74 = ISOGONAL CONJUGATE OF EULER INFINITY POINT (0.7484, -0.3437) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_339 = ISOTOMIC CONJUGATE OF X(250) (0.6002, 0.0170) X_111 = PARRY POINT (0.9885, -0.0457) X_459 = -CEVA CONJUGATE OF X(4) (0.5934, 0.8103) X_403 = OF THE ORTHIC TRIANGLE (0.7040, 0.6358) X_842 = ISOGONAL CONJUGATE OF X(542) (-0.0101, 0.1156) X_1289 = COLLINGS TRANSFORM OF X(25) (0.6436, 0.5918) A B C X24 X98 X4 X127 X66 X74 X25 X339 X111 X459 X403 X842 X1289 (a, b, c) = (5, 6, 7) | AB = 1

X1289 (COLLINGS TRANSFORM OF X25) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(\tan A \csc(B - C)/(\sin 2A - \tan \omega ) : :\)
Search Value (6, 9, 13): \(0.631528825043\)

X1289 lies on the circumcircle.

▸ Incident Central Lines8 lines

{4, 127}, {24, 98}, {25, 339}, {66, 74}, {111, 459}, {378, 1294}, {403, 842}, {648, 827}

▸ Functional Relations9 relations