X833

o-(1, 4) CIRCUMCIRCLE POINT

X833 = isogonal conjugate of X832
< 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) { 106, 977 }: Central Line L(106, 977) { 759, 1010 }: Central Line L(759, 1010) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_832 = ODD (1, 4) INFINITY POINT (1.0668, -0.0533) X_106 = Λ(INCENTER, CENTROID) (1.0000, 0.0000) X_977 = ISOGONAL CONJUGATE OF X(976) (0.5890, 0.2525) X_759 = EVEN (1, 3) CIRCUMCIRCLE POINT (0.9498, -0.1389) X_1010 = INTERCEPT OF EULER LINE AND LINE X(1)X(75) (0.5391, 0.2043) X_833 = o-(1, 4) CIRCUMCIRCLE POINT (0.1829, 0.5019) A B C X832 X106 X977 X759 X1010 X833 (a, b, c) = (5, 6, 7) | AB = 1

X833 (o-(1, 4) CIRCUMCIRCLE POINT) 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 \(f(a,b,c) = 1/[a^{0}(b^{4} - c^{4}) + a^{3}(b^{1} - c^{1})]\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(1.915147865901\)

X833 lies on the circumcircle.

▸ Incident Central Lines2 lines

{106, 977}, {759, 1010}

▸ Functional Relations3 relations