X746

EVEN (- 1, 4) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X746 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, 75 }: Central Line L(32, 75) { 192, 315 }: Central Line L(192, 315) { 30, 511 }: Central Line L(30, 511) { 37, 626 }: Central Line L(37, 626) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_747 = EVEN (- 1, 4) CIRCUMCIRCLE POINT (0.9745, -0.0859) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_192 = -CEVA CONJUGATE OF X(2) (CONGRUENT PARALLELIANS POINT) (0.6147, 0.2635) 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_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_626 = COMPLEMENT OF X(32) (0.4861, 0.1333) X_746 = EVEN (- 1, 4) INFINITY POINT (0.1559, -0.2460) A B C X747 X32 X75 X192 X315 X30 X511 X37 X626 X746 (a, b, c) = (5, 6, 7) | AB = 1

X746 (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 \(f(a,b,c) = a ^{-2}(b^{4} + c^{4}) - a^{3}(b ^{-1} + c ^{-1})\)
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

{30, 511}, {32, 75}, {37, 626}, {192, 315}

▸ Functional Relations1 relation