X702

EVEN (- 4, 0) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X702 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) { 2, 308 }: Central Line L(2, 308) { 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_703 = EVEN (- 4, 0) CIRCUMCIRCLE POINT (1.0008, 0.2001) X_2 = CENTROID (0.5374, 0.2000) X_308 = ISOTOMIC CONJUGATE OF X(39) (0.4915, 0.1700) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_702 = EVEN (- 4, 0) INFINITY POINT (0.0459, -0.1206) A B C X703 X2 X308 X30 X511 X702 (a, b, c) = (5, 6, 7) | AB = 1

X702 (EVEN (- 4, 0) 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 \(f(a,b,c) = a ^{-5}(b^{0} + c^{0}) - a ^{-1}(b ^{-4} + c ^{-4})\)
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

{2, 308}, {30, 511}

▸ Functional Relations1 relation