X3011

(NAGEL LINE)∩(ORTHIC AXIS)

X3011 = complement of X3006
< A B C >: Reference Triangle △ABC < M_a M_b M_c >: Medial Triangle △M_a M_b M_c [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 2, 3006 }: Nagel Line { 1, 2 }: Nagel Line { 25, 225 }: Central Line L(25, 225) { 31, 226 }: Central Line L(31, 226) { 230, 231 }: Central Line L(230, 231) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) M_a = Midpoint M_a of BC (0.8061, 0.2999) M_b = Midpoint M_b of CA (0.3061, 0.2999) M_c = Midpoint M_c of AB (0.5000, 0.0000) X_2 = CENTROID (0.5374, 0.2000) X_3006 = (DE LONGCHAMPS LINE)∩(NAGEL LINE) (-0.3980, -0.7165) X_1 = INCENTER (0.5714, 0.2333) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_225 = -CEVA CONJUGATE OF X(65) (0.6246, 0.4451) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_226 = -CEVA CONJUGATE OF X(65) (0.5778, 0.2588) X_230 = -CEVA CONJUGATE OF X(114) (0.9746, 0.6698) X_231 = -CEVA CONJUGATE OF X(128) (1.0375, 0.6458) X_3011 = (NAGEL LINE)∩(ORTHIC AXIS) (1.0051, 0.6582) A B C Ma Mb Mc X2 X3006 X1 X25 X225 X31 X226 X230 X231 X3011 (a, b, c) = (5, 6, 7) | AB = 1

X3011 ((NAGEL LINE)∩(ORTHIC AXIS)) 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 \(f(a,b,c) = bc[2a^{3} + (b + c)(b - c + a)(b - c - a)]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.022251357905\)
▸ Incident Central Lines17 lines

{1, 2}, {3, 1072}, {11, 1279}, {12, 1104}, {25, 225}, {31, 226}, {100, 1738}, {105, 2006}, {111, 2690}, {142, 750}, {230, 231}, {238, 908}, {459, 1068}, {851, 2223}, {1447, 1758}, {1612, 1838}, {1836, 3049}

▸ Functional Relations6 relations