X754

EVEN (0, 4) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X754 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, 32 }: Central Line L(2, 32) { 115, 316 }: Central Line L(115, 316) { 187, 325 }: Central Line L(187, 325) { 30, 511 }: Central Line L(30, 511) { 230, 625 }: Central Line L(230, 625) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_755 = EVEN (0, 4) CIRCUMCIRCLE POINT (0.9524, -0.1340) X_2 = CENTROID (0.5374, 0.2000) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_115 = CENTER OF KIEPERT HYPERBOLA (0.7507, 0.0838) X_316 = DROUSSENT PIVOT (-0.7850, -1.9118) X_187 = INVERSE-IN-CIRCUMCIRCLE OF X(6) (SCHOUTE CENTER) (1.1986, 1.2559) X_325 = -HIRST INVERSE OF X(69) (-0.3370, -0.7398) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_230 = -CEVA CONJUGATE OF X(114) (0.9746, 0.6698) X_625 = MIDPOINT OF X(623) AND X(624) (0.2068, -0.3280) X_754 = EVEN (0, 4) INFINITY POINT (0.1795, -0.2651) A B C X755 X2 X32 X115 X316 X187 X325 X30 X511 X230 X625 X754 (a, b, c) = (5, 6, 7) | AB = 1

X754 (EVEN (0, 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 \(f(a,b,c) = a ^{-1}(b^{4} + c^{4}) - a^{3}(b^{0} + c^{0})\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
▸ Incident Central Lines5 lines

{2, 32}, {30, 511}, {115, 316}, {187, 325}, {230, 625}

▸ Functional Relations1 relation