X3081

DANNEELS POINT OF X30

X3081 = reflection of X1650 in X1651
< 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) { 1650, 1651 }: Euler Line { 2, 3 }: Euler Line A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1650 = TRIPOLAR CENTROID OF X(525) (0.4551, -0.0155) X_1651 = TRIPOLAR CENTROID OF X(648) (0.6197, 0.4154) X_2 = CENTROID (0.5374, 0.2000) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_3081 = DANNEELS POINT OF X(30) (0.7844, 0.8462) A B C X1650 X1651 X2 X3 X3081 (a, b, c) = (5, 6, 7) | AB = 1

X3081 (DANNEELS POINT OF X30) 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 \(f(a,b,c) = a u^{2}(bv + cw)\), where \(u : v : w\) = X30
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.704134108907\)
▸ Incident Central Lines1 line

{2, 3}

▸ Functional Relations4 relations

Notes

As a point on the Euler line, X3081 has Shinagawa coefficients \((27F^{2} - S^{2}, -27(E + F)F + 9S^{2})\).