X466

EULER LINE INTERCEPT OF LINE X216X_396

X446 = complement of X472
< 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, 472 }: Euler Line { 2, 3 }: Euler Line { 216, 396 }: Central Line L(216, 396) { 395, 577 }: Central Line L(395, 577) 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_472 = -CROSS CONJUGATE OF X(303) (0.6350, 0.4553) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_216 = -CEVA CONJUGATE OF X(51) (0.5201, 0.1353) X_396 = MIDPOINT OF X(13) AND X(15) (0.5699, 0.2349) X_395 = MIDPOINT OF X(14) AND X(16) (1.3794, 1.1048) X_577 = HARMONIC OF X(216) (0.4663, 0.0464) X_466 = EULER LINE INTERCEPT OF LINE X(216)X(396) (0.4886, 0.0723) A B C Ma Mb Mc X2 X472 X3 X216 X396 X395 X577 X466 (a, b, c) = (5, 6, 7) | AB = 1

X466 (EULER LINE INTERCEPT OF LINE X216X_396) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(u \cot A : v \cot B : w \cot C\), where \(u : v : w\) = X398; e.g., \(u(A,B,C) = \cos(B - C) - 2 \cos(A - \pi /3)\)
Barycentrics: \(u \cos A : v \cos B : w \cos C\)
Search Value (6, 9, 13): \(3.717116127581\)
▸ Incident Central Lines3 lines

{2, 3}, {216, 396}, {395, 577}

▸ Functional Relations2 relations

Notes

As a point on the Euler line, X466 has Shinagawa coefficients \((2F - 3^{1/2}S, 3^{1/2}S)\).

X466 is the {X2,X3}-harmonic conjugate of X465.