X1728

MIMOSA TRANSFORM OF X84

X1728 = X4-aleph conjugate of X1720
< 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) { 1, 6 }: Incenter–Symmedian Line { 4, 46 }: Central Line L(4, 46) { 5, 57 }: Central Line L(5, 57) { 33, 580 }: Central Line L(33, 580) { 226, 499 }: Central Line L(226, 499) { 63, 1210 }: Central Line L(63, 1210) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_4 = ORTHOCENTER (0.6122, 0.3958) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_580 = ORTHOGONAL OF X(284) (0.7089, 0.4470) X_226 = -CEVA CONJUGATE OF X(65) (0.5778, 0.2588) X_499 = {X(1),X(2)}-HARMONIC CONJUGATE OF X(498) (0.4458, 0.1102) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_1210 = ISOGONAL CONJUGATE OF X(1167) (0.6144, 0.2754) X_1728 = MIMOSA TRANSFORM OF X(84) (0.8649, 0.5819) A B C X1 X6 X4 X46 X5 X57 X33 X580 X226 X499 X63 X1210 X1728 (a, b, c) = (5, 6, 7) | AB = 1

X1728 (MIMOSA TRANSFORM OF X84) 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 \(f(a,b,c) = - (\cos A)/x + (\cos B)/y + (\cos C)/z\),\(x : y : z\) = X84
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.256125765207\)
▸ Incident Central Lines13 lines

{1, 6}, {3, 1864}, {4, 46}, {5, 57}, {33, 580}, {36, 1490}, {40, 1837}, {63, 1210}, {84, 1750}, {226, 499}, {1707, 1771}, {1711, 1720}, {1712, 1714}

▸ Functional Relations1 relation