X1753

MIMOSA TRANSFORM OF X280

X1753 = X92-aleph conjugate of X1767
< 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, 9 }: Orthocenter–Spieker Line { 3, 33 }: Central Line L(3, 33) { 46, 208 }: Central Line L(46, 208) { 63, 318 }: Central Line L(63, 318) { 34, 517 }: Central Line L(34, 517) { 204, 580 }: Central Line L(204, 580) 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_9 = MITTENPUNKT (0.5110, 0.1615) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_208 = -CEVA CONJUGATE OF X(34) (0.6242, -0.2728) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_318 = ISOTOMIC CONJUGATE OF X(77) (0.5514, 0.2839) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8180, 0.7154) X_204 = -CEVA CONJUGATE OF X(19) (0.6683, 3.3982) X_580 = ORTHOGONAL OF X(284) (0.7089, 0.4470) X_1753 = MIMOSA TRANSFORM OF X(280) (0.7066, 0.6139) A B C X4 X9 X3 X33 X46 X208 X63 X318 X34 X517 X204 X580 X1753 (a, b, c) = (5, 6, 7) | AB = 1

X1753 (MIMOSA TRANSFORM OF X280) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = - (\cos A)/x + (\cos B)/y + (\cos C)/z\),\(x : y : z\) = X280
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(7.563496281653\)
▸ Incident Central Lines16 lines

{1, 947}, {3, 33}, {4, 9}, {34, 517}, {46, 208}, {55, 1887}, {63, 318}, {204, 580}, {225, 1217}, {475, 946}, {1068, 1435}, {1158, 1726}, {1445, 1895}, {1593, 1824}, {1597, 1871}, {1708, 1712}

▸ Functional Relations2 relations