X1765

MIMOSA TRANSFORM OF X333

< 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) { 3, 9 }: Central Line L(3, 9) { 63, 321 }: Central Line L(63, 321) { 20, 391 }: Central Line L(20, 391) { 71, 515 }: Central Line L(71, 515) { 21, 572 }: Central Line L(21, 572) { 6, 1012 }: Central Line L(6, 1012) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_9 = MITTENPUNKT (0.5110, 0.1615) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_321 = ISOTOMIC CONJUGATE OF X(81) (0.4800, 0.1527) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_391 = INTERSECTION OF LINES X(2,6) AND X(8,9) (0.4857, 0.1443) X_71 = ISOGONAL CONJUGATE OF X(27) (0.4807, 0.0915) X_515 = ISOGONAL CONJUGATE OF X(102) (0.6804, 0.7691) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_572 = ORTHOGONAL OF X(58) (7.2953, -0.6907) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_1012 = INTERCEPT OF EULER LINE AND LINE X(1)X(84) (0.5770, 0.3036) X_1765 = MIMOSA TRANSFORM OF X(333) (0.5463, 0.3524) A B C X3 X9 X63 X321 X20 X391 X71 X515 X21 X572 X6 X1012 X1765 (a, b, c) = (5, 6, 7) | AB = 1

X1765 (MIMOSA TRANSFORM OF X333) 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 \(f(a,b,c) = - (\cos A)/x + (\cos B)/y + (\cos C)/z\),\(x : y : z\) = X333
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-11.892929716686\)
▸ Incident Central Lines14 lines

{1, 1409}, {3, 9}, {6, 1012}, {7, 1020}, {19, 1158}, {20, 391}, {21, 572}, {63, 321}, {71, 515}, {580, 1778}, {608, 1777}, {1707, 1709}, {1735, 1880}, {1768, 1781}

▸ Functional Relations1 relation