X1972

TRILINEAR POLE OF PU(38)

X1972 = reflection of X648 in X216
< 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, 216 }: Central Line L(648, 216) { 95, 216 }: Central Line L(95, 216) { 287, 401 }: Central Line L(287, 401) { 925, 1298 }: Central Line L(925, 1298) 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_216 = -CEVA CONJUGATE OF X(51) (0.5201, 0.1353) X_95 = CEVAPOINT OF CENTROID AND CIRCUMCENTER (0.5172, 0.1562) X_287 = -HIRST INVERSE OF X(98) (0.7437, -0.0511) X_401 = BAILEY POINT (-0.0758, -1.4044) X_925 = ANTICOMPLEMENT OF X(136) (0.0074, -0.0312) X_1298 = COLLINGS TRANSFORM OF X(130) (0.6949, -0.3696) X_1972 = TRILINEAR POLE OF PU(38) (0.5839, -0.3149) A B C X648 X216 X95 X287 X401 X925 X1298 X1972 (a, b, c) = (5, 6, 7) | AB = 1

X1972 (TRILINEAR POLE OF PU(38)) 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 \(f(a,b,c) = bc/(\sin^{2} 2A - \sin 2B \sin 2C)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.008032397262\)
▸ Incident Central Lines3 lines

{95, 216}, {287, 401}, {925, 1298}

▸ Functional Relations5 relations