X736

EVEN (- 2, 4) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X736 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) { 32, 76 }: Central Line L(32, 76) { 39, 325 }: Central Line L(39, 325) { 194, 315 }: Central Line L(194, 315) { 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_737 = EVEN (- 2, 4) CIRCUMCIRCLE POINT (0.9903, -0.0393) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_325 = -HIRST INVERSE OF X(69) (-0.3370, -0.7398) X_194 = -CEVA CONJUGATE OF X(2) (0.6989, 0.3222) 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_736 = EVEN (- 2, 4) INFINITY POINT (0.9400, 0.6270) A B C X737 X32 X76 X39 X325 X194 X315 X30 X511 X736 (a, b, c) = (5, 6, 7) | AB = 1

X736 (EVEN (- 2, 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 \(f(a,b,c) = a ^{-3}(b^{4} + c^{4}) - a^{3}(b ^{-2} + c ^{-2})\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
▸ Alternate Coordinates1 form

  • Barycentrics: \(a^{6} (b^{2} + c^{2}) - b^{2} c^{2} (b^{4} + c^{4}) : :\)

▸ Incident Central Lines4 lines

{30, 511}, {32, 76}, {39, 325}, {194, 315}

▸ Functional Relations1 relation