X3199

X53-CEVA CONJUGATE OF X51

X3199 = X53-Ceva conjugate of X51
< 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, 39 }: Central Line L(4, 39) { 25, 32 }: Central Line L(25, 32) { 5, 53 }: Central Line L(5, 53) { 24, 187 }: Central Line L(24, 187) { 51, 217 }: Central Line L(51, 217) { 115, 235 }: Central Line L(115, 235) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_53 = SYMMEDIAN POINT OF ORTHIC TRIANGLE (0.6164, 0.4390) X_51 = CENTROID OF ORTHIC TRIANGLE (0.6093, 0.3186) X_4 = ORTHOCENTER (0.6122, 0.3958) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_24 = PERSPECTOR OF ABC AND ORTHIC-OF-ORTHIC TRIANGLE (0.6627, 0.5278) X_187 = INVERSE-IN-CIRCUMCIRCLE OF X(6) (SCHOUTE CENTER) (1.1986, 1.2559) X_217 = -CEVA CONJUGATE OF X(51) (0.5928, 0.1915) X_115 = CENTER OF KIEPERT HYPERBOLA (0.7507, 0.0838) X_235 = -CEVA CONJUGATE OF X(185) (0.6375, 0.4618) X_3199 = -CEVA CONJUGATE OF X(51) (0.6307, 0.4844) A B C X53 X51 X4 X39 X25 X32 X5 X24 X187 X217 X115 X235 X3199 (a, b, c) = (5, 6, 7) | AB = 1

X3199 (X53-CEVA CONJUGATE OF X51) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(u(-u/x + v/y + w/z) : v(u/x - v/y + w/z) : w(u/x + v/y - w/z)\), where \(x : y : z\) = X53 and \(u : v : w\) = X51
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\), where \(f(a,b,c) = u(-u/x + v/y + w/z)\)
Search Value (6, 9, 13): \(-0.028647965079\)
▸ Incident Central Lines20 lines

{4, 39}, {5, 53}, {6, 1598}, {24, 187}, {25, 32}, {33, 1500}, {34, 1015}, {51, 217}, {52, 1626}, {97, 2984}, {115, 235}, {297, 626}, {393, 800}, {427, 1506}, {574, 1593}, {1504, 3092}, {1505, 3093}, {1574, 1861}, {1692, 1974}, {1843, 2211}

▸ Functional Relations7 relations