X3193

X29-CEVA CONJUGATE OF X21

X3193 = X29-Ceva conjugate of X21
< 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, 21 }: Central Line L(1, 21) { 28, 110 }: Central Line L(28, 110) { 4, 155 }: Central Line L(4, 155) { 46, 453 }: Central Line L(46, 453) { 377, 394 }: Central Line L(377, 394) { 225, 651 }: Central Line L(225, 651) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_29 = CEVAPOINT OF INCENTER AND ORTHOCENTER (0.5903, 0.3384) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_1 = INCENTER (0.5714, 0.2333) X_28 = CEVAPOINT OF X(19) AND X(25) (0.6285, 0.4382) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_4 = ORTHOCENTER (0.6122, 0.3958) X_155 = EIGENCENTER OF ORTHIC TRIANGLE (1.1658, 0.5033) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_453 = POINT ALSHAIN (0.6610, 0.5233) X_377 = EULER LINE INTERCEPT OF LINE X(7)X(8) (0.5473, 0.2258) X_394 = -CEVA CONJUGATE OF X(3) (0.3778, 0.0284) X_225 = -CEVA CONJUGATE OF X(65) (0.6246, 0.4451) X_651 = TRILINEAR POLE OF LINE X(1)X(3) (0.3048, 0.5599) X_3193 = -CEVA CONJUGATE OF X(21) (0.7094, 0.4146) A B C X29 X21 X1 X28 X110 X4 X155 X46 X453 X377 X394 X225 X651 X3193 (a, b, c) = (5, 6, 7) | AB = 1

X3193 (X29-CEVA CONJUGATE OF X21) 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 \(x : y : z\) = X29 and \(u : v : w\) = X21
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): \(38.351818975126\)
▸ Incident Central Lines17 lines

{1, 21}, {4, 155}, {28, 110}, {29, 1069}, {40, 1790}, {46, 453}, {57, 1819}, {225, 651}, {323, 2475}, {377, 394}, {517, 1437}, {648, 1896}, {1068, 3157}, {1331, 3191}, {1442, 1444}, {1816, 1936}, {2287, 2323}

▸ Functional Relations4 relations