X760

EVEN (1, 4) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X760 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) { 1, 32 }: Central Line L(1, 32) { 8, 315 }: Central Line L(8, 315) { 30, 511 }: Central Line L(30, 511) { 10, 626 }: Central Line L(10, 626) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_761 = EVEN (1, 4) CIRCUMCIRCLE POINT (0.9239, -0.1820) X_1 = INCENTER (0.5714, 0.2333) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_8 = NAGEL POINT (0.4694, 0.1333) X_315 = ISOTOMIC CONJUGATE OF X(66) (0.3323, -0.0666) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_626 = COMPLEMENT OF X(32) (0.4861, 0.1333) X_760 = EVEN (1, 4) INFINITY POINT (0.2055, -0.2840) A B C X761 X1 X32 X8 X315 X30 X511 X10 X626 X760 (a, b, c) = (5, 6, 7) | AB = 1

X760 (EVEN (1, 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 \(f(a,b,c) = a^{0}(b^{4} + c^{4}) - a^{3}(b^{1} + c^{1})\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
▸ Incident Central Lines4 lines

{1, 32}, {8, 315}, {10, 626}, {30, 511}

▸ Functional Relations2 relations