X824

ODD (0, 3) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X824 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) { 321, 693 }: Central Line L(321, 693) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_825 = o-(0, 3) CIRCUMCIRCLE POINT (0.2886, 0.5665) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_321 = ISOTOMIC CONJUGATE OF X(81) (0.4800, 0.1527) X_693 = ISOTOMIC CONJUGATE OF X(100) (-25.8163, 8.9981) X_824 = ODD (0, 3) INFINITY POINT (1.0936, 0.0129) A B C X825 X30 X511 X321 X693 X824 (a, b, c) = (5, 6, 7) | AB = 1

X824 (ODD (0, 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 \(f(a,b,c) = a ^{-1}(b^{3} - c^{3}) + a^{2}(b^{0} - c^{0})\)
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}, {321, 693}

▸ Functional Relations3 relations