X830

ODD (1, 3) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X830 lies on the line at infinity.
< 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) { 30, 511 }: Central Line L(30, 511) { 661, 1580 }: Central Line L(661, 1580) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_831 = o-(1, 3) CIRCUMCIRCLE POINT (0.1595, 0.4822) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_661 = CROSSDIFFERENCE OF X(1) AND X(21) (48.4286, -23.0952) X_1580 = POINT ALUDRA (1.3094, 1.2033) X_830 = ODD (1, 3) INFINITY POINT (1.0590, -0.0690) A B C X831 X30 X511 X661 X1580 X830 (a, b, c) = (5, 6, 7) | AB = 1

X830 (ODD (1, 3) INFINITY 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 \(f(a,b,c) = a^{0}(b^{3} - c^{3}) + a^{2}(b^{1} - c^{1})\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
▸ Incident Central Lines2 lines

{30, 511}, {661, 1580}

▸ Functional Relations2 relations