X714

EVEN (- 3, - 1) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X714 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) { 38, 75 }: Central Line L(38, 75) { 30, 511 }: Central Line L(30, 511) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_715 = EVEN (- 3, - 1) CIRCUMCIRCLE POINT (1.0000, 0.2040) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_714 = EVEN (- 3, - 1) INFINITY POINT (1.0302, 0.5186) A B C X715 X38 X75 X30 X511 X714 (a, b, c) = (5, 6, 7) | AB = 1

X714 (EVEN (- 3, - 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 \(f(a,b,c) = a ^{-4}(b ^{-1} + c ^{-1}) - a ^{-2}(b ^{-3} + c ^{-3})\)
Barycentrics: \((b + c) (a^{2} (b^{2} - b c + c^{2}) - b^{2} c^{2}) : :\)
▸ Incident Central Lines2 lines

{30, 511}, {38, 75}

▸ Functional Relations1 relation