X305

ISOTOMIC CONJUGATE OF X25

X305 is the isotomic conjugate of X25.
< 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) { 2, 39 }: Central Line L(2, 39) { 22, 99 }: Central Line L(22, 99) { 95, 183 }: Central Line L(95, 183) { 264, 325 }: Central Line L(264, 325) { 304, 306 }: Central Line L(304, 306) { 287, 394 }: Central Line L(287, 394) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_2 = CENTROID (0.5374, 0.2000) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_22 = EXETER POINT (0.4143, -0.1221) X_99 = STEINER POINT (0.1109, 0.4322) X_95 = CEVAPOINT OF CENTROID AND CIRCUMCENTER (0.5172, 0.1562) X_183 = TRILINEAR PRODUCT X(75)X(182) (0.4700, 0.1275) X_264 = ISOTOMIC CONJUGATE OF CIRCUMCENTER (0.5720, 0.3293) X_325 = -HIRST INVERSE OF X(69) (-0.3370, -0.7398) X_304 = ISOTOMIC CONJUGATE OF X(19) (0.3683, 0.0513) X_306 = ISOTOMIC CONJUGATE OF X(27) (0.3924, 0.0579) X_287 = -HIRST INVERSE OF X(98) (0.7437, -0.0511) X_394 = -CEVA CONJUGATE OF X(3) (0.3778, 0.0284) X_305 = ISOTOMIC CONJUGATE OF X(25) (0.3258, 0.0397) A B C X25 X2 X39 X22 X99 X95 X183 X264 X325 X304 X306 X287 X394 X305 (a, b, c) = (5, 6, 7) | AB = 1

X305 (ISOTOMIC CONJUGATE OF X25) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(b^{4}c^{4}\cos A : c^{4}a^{4}\cos B : a^{4}b^{4}\cos C\)
Barycentrics: \(b^{3}c^{3}\cos A : c^{3}a^{3}\cos B : a^{3}b^{3}\cos C\)
Search Value (6, 9, 13): \(6.541981036071\)
▸ Alternate Coordinates1 form

  • Trilinears: \(\cot A \csc(A - \omega ) : \cot B \csc(B - \omega ) : \cot C \csc(C - \omega )\)

▸ Incident Central Lines11 lines

{2, 39}, {22, 99}, {25, 683}, {95, 183}, {264, 325}, {287, 394}, {304, 306}, {311, 1007}, {341, 1088}, {350, 614}, {561, 1441}

▸ Functional Relations7 relations