X287

X2-HIRST INVERSE OF X98

X287 is the X2-hirst inverse of X98.
< 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) { 648, 6 }: Central Line L(648, 6) { 2, 98 }: Central Line L(2, 98) { 95, 141 }: Central Line L(95, 141) { 6, 264 }: Central Line L(6, 264) { 83, 217 }: Central Line L(83, 217) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_648 = TRILINEAR POLE OF EULER LINE (0.4563, 0.5855) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_2 = CENTROID (0.5374, 0.2000) X_98 = TARRY POINT (0.8891, -0.2281) X_95 = CEVAPOINT OF CENTROID AND CIRCUMCENTER (0.5172, 0.1562) X_141 = COMPLEMENT OF SYMMEDIAN POINT (0.5061, 0.1663) X_264 = ISOTOMIC CONJUGATE OF CIRCUMCENTER (0.5720, 0.3293) X_83 = CEVAPOINT OF CENTROID AND SYMMEDIAN POINT (0.5651, 0.2360) X_217 = -CEVA CONJUGATE OF X(51) (0.5928, 0.1915) X_287 = -HIRST INVERSE OF X(98) (0.7437, -0.0511) A B C X648 X6 X2 X98 X95 X141 X264 X83 X217 X287 (a, b, c) = (5, 6, 7) | AB = 1

X287 (X2-HIRST INVERSE OF X98) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(\cot A \sec(A + \omega ) : \cot B \sec(B + \omega ) : \cot C \sec(C + \omega )\)
Barycentrics: \(\cos A \sec(A + \omega ) : \cos B \sec(B + \omega ) : \cos C \sec(C + \omega )\)
Search Value (6, 9, 13): \(2.948985116427\)

X287 lies on the MacBeath circumconic.

▸ Incident Central Lines13 lines

{2, 98}, {6, 264}, {69, 248}, {83, 217}, {95, 141}, {185, 384}, {193, 253}, {293, 306}, {297, 685}, {305, 394}, {401, 511}, {651, 894}, {879, 895}

▸ Functional Relations15 relations