X734

EVEN (- 2, 3) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X734 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) { 31, 76 }: Central Line L(31, 76) { 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_735 = EVEN (- 2, 3) CIRCUMCIRCLE POINT (1.0005, 0.0024) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_734 = EVEN (- 2, 3) INFINITY POINT (0.1172, -0.2097) A B C X735 X31 X76 X30 X511 X734 (a, b, c) = (5, 6, 7) | AB = 1

X734 (EVEN (- 2, 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 \(f(a,b,c) = a ^{-3}(b^{3} + c^{3}) - a^{2}(b ^{-2} + c ^{-2})\)
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}, {31, 76}

▸ Functional Relations1 relation