X1791

INVERSE MIMOSA TRANSFORM OF X10

X1791 = isogonal conjugate of X1829
< 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, 12 }: Central Line L(2, 12) { 21, 37 }: Central Line L(21, 37) { 48, 78 }: Central Line L(48, 78) { 8, 197 }: Central Line L(8, 197) { 63, 201 }: Central Line L(63, 201) { 3, 345 }: Central Line L(3, 345) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1829 = ZOSMA TRANSFORM OF X(10) (0.6233, 0.4161) X_2 = CENTROID (0.5374, 0.2000) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5412, 0.1246) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_8 = NAGEL POINT (0.4694, 0.1333) X_197 = -CEVA CONJUGATE OF X(6) (0.4333, -0.1633) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_201 = -CEVA CONJUGATE OF X(12) (0.4897, 0.1062) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_345 = ISOTOMIC CONJUGATE OF X(278) (0.3405, 0.0381) X_1791 = INVERSE MIMOSA TRANSFORM OF X(10) (0.4638, 0.0876) A B C X1829 X2 X12 X21 X37 X48 X78 X8 X197 X63 X201 X3 X345 X1791 (a, b, c) = (5, 6, 7) | AB = 1

X1791 (INVERSE MIMOSA TRANSFORM OF X10) 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 \(f(a,b,c) = (\cos A)/(y + z)\);\(x : y : z\) = X10
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(6.369449761393\)
▸ Incident Central Lines11 lines

{1, 1472}, {2, 12}, {3, 345}, {8, 197}, {21, 37}, {48, 78}, {63, 201}, {72, 1437}, {228, 1792}, {280, 1436}, {975, 993}

▸ Functional Relations2 relations