X3549

EULER LINE INTERCEPT OF LINE X68X_184

X3549 = complement of X3541
< 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, 3541 }: Euler Line { 2, 3 }: Euler Line { 68, 184 }: Central Line L(68, 184) { 193, 195 }: Central Line L(193, 195) { 155, 343 }: Central Line L(155, 343) { 206, 1209 }: Central Line L(206, 1209) 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_3541 = EULER LINE INTERCEPT OF LINE X(33)X(499) (0.5885, 0.3336) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_68 = PRASOLOV POINT (-0.0535, -0.0055) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_193 = -CEVA CONJUGATE OF X(2) (0.7878, 0.4690) X_195 = -CEVA CONJUGATE OF X(3) (0.6761, 0.3331) X_155 = EIGENCENTER OF ORTHIC TRIANGLE (1.1658, 0.5033) X_343 = ISOTOMIC CONJUGATE OF X(275) (0.4345, 0.0893) X_206 = -CEVA CONJUGATE OF X(32) (0.5105, -0.2297) X_1209 = ISOGONAL CONJUGATE OF X(1166) (0.5121, 0.1912) X_3549 = EULER LINE INTERCEPT OF LINE X(68)X(184) (0.5119, 0.1331) A B C Ma Mb Mc X2 X3541 X3 X68 X184 X193 X195 X155 X343 X206 X1209 X3549 (a, b, c) = (5, 6, 7) | AB = 1

X3549 (EULER LINE INTERCEPT OF LINE X68X_184) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(\sec B \sec C + 4 \sin B \sin C : :\)
Search Value (6, 9, 13): \(-1.145971744862\)
▸ Incident Central Lines9 lines

{2, 3}, {68, 184}, {155, 343}, {193, 195}, {206, 1209}, {216, 2165}, {498, 1062}, {499, 1060}, {577, 1506}

▸ Functional Relations2 relations

  • X3549 = complement of X3541

  • X3549 = homothetic center of orthocevian triangle of X2 and Johnson triangle

Notes

As a point on the Euler line, X3549 has Shinagawa coefficients \((E + 4F, -E)\).