X464

EULER LINE INTERCEPT OF LINE X63X_69

X464 is the {X2,X20}-harmonic conjugate of X27.
< 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, 20 }: Euler Line { 63, 69 }: Central Line L(63, 69) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_27 = CEVAPOINT OF ORTHOCENTER AND CLAWSON CENTER (0.6182, 0.4112) X_2 = CENTROID (0.5374, 0.2000) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_464 = EULER LINE INTERCEPT OF LINE X(63)X(69) (0.4986, 0.0983) A B C X27 X2 X20 X63 X69 X464 (a, b, c) = (5, 6, 7) | AB = 1

X464 (EULER LINE INTERCEPT OF LINE X63X_69) 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 \(u : v : w\) = X387
Barycentrics: \(u \cos A : v \cos B : w \cos C\)
Search Value (6, 9, 13): \(5.837181788574\)
▸ Incident Central Lines2 lines

{2, 3}, {63, 69}

Notes

As a point on the Euler line, X464 has Shinagawa coefficients \((E + \$bc\$, -E - F - \$bc\$)\).