X461

EULER LINE INTERCEPT OF LINE X33X_200

< 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) { 2, 3 }: Euler Line { 33, 200 }: Central Line L(33, 200) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_4 = ORTHOCENTER (0.6122, 0.3958) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_200 = -CEVA CONJUGATE OF X(9) (0.4392, 0.1037) X_461 = EULER LINE INTERCEPT OF LINE X(33)X(200) (0.5888, 0.3344) A B C X2 X3 X4 X33 X200 X461 (a, b, c) = (5, 6, 7) | AB = 1

X461 (EULER LINE INTERCEPT OF LINE X33X_200) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(u \tan A : v \tan B : w \tan C\), where \(u : v : w\) = X391; e.g., \(u(a,b,c) = bc(3a + b + c)(b + c - a)\)
Barycentrics: \(u \sin A \tan A : v \sin B \tan B : w \sin C \tan C\)
Search Value (6, 9, 13): \(5.102425681601\)
▸ Incident Central Lines2 lines

{2, 3}, {33, 200}

Notes

As a point on the Euler line, X461 has Shinagawa coefficients \((2F,\$bc\$ - E - F)\).