X700

EVEN (- 4, - 1) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X700 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) { 75, 871 }: Central Line L(75, 871) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_701 = EVEN (- 4, - 1) CIRCUMCIRCLE POINT (0.9924, 0.2359) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_871 = ISOTOMIC CONJUGATE OF X(869) (0.4515, 0.1398) X_700 = EVEN (- 4, - 1) INFINITY POINT (0.0346, -0.1027) A B C X701 X30 X511 X75 X871 X700 (a, b, c) = (5, 6, 7) | AB = 1

X700 (EVEN (- 4, - 1) 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 \(f(a,b,c) = a ^{-5}(b ^{-1} + c ^{-1}) - a ^{-2}(b ^{-4} + c ^{-4})\)
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}, {75, 871}

▸ Functional Relations1 relation