X766

EVEN (3, 4) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X766 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, 32 }: Central Line L(31, 32) { 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_767 = EVEN (3, 4) CIRCUMCIRCLE POINT (0.8487, -0.2706) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_766 = EVEN (3, 4) INFINITY POINT (0.2628, -0.3187) A B C X767 X31 X32 X30 X511 X766 (a, b, c) = (5, 6, 7) | AB = 1

X766 (EVEN (3, 4) 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 \(f(a,b,c) = a^{2}(b^{4} + c^{4}) - a^{3}(b^{3} + c^{3})\)
▸ Incident Central Lines2 lines

{30, 511}, {31, 32}

▸ Functional Relations2 relations