X712

EVEN (- 3, - 2) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X712 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) { 76, 321 }: Central Line L(76, 321) { 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_713 = EVEN (- 3, - 2) CIRCUMCIRCLE POINT (0.9916, 0.2389) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_321 = ISOTOMIC CONJUGATE OF X(81) (0.4800, 0.1527) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_712 = EVEN (- 3, - 2) INFINITY POINT (0.0337, -0.1011) A B C X713 X76 X321 X30 X511 X712 (a, b, c) = (5, 6, 7) | AB = 1

X712 (EVEN (- 3, - 2) 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 \(f(a,b,c) = a ^{-4}(b ^{-2} + c ^{-2}) - a ^{-3}(b ^{-3} + c ^{-3})\)
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}, {76, 321}

▸ Functional Relations1 relation