X698

EVEN (- 4, - 2) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X698 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) { 6, 194 }: Central Line L(6, 194) { 76, 141 }: Central Line L(76, 141) { 75, 257 }: Central Line L(75, 257) { 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_699 = EVEN (- 4, - 2) CIRCUMCIRCLE POINT (0.9822, 0.2692) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_194 = -CEVA CONJUGATE OF X(2) (0.6989, 0.3222) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_141 = COMPLEMENT OF SYMMEDIAN POINT (0.5061, 0.1663) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_257 = ISOGONAL CONJUGATE OF X(172) (0.5240, 0.1822) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_698 = EVEN (- 4, - 2) INFINITY POINT (1.0503, 0.4852) A B C X699 X6 X194 X76 X141 X75 X257 X30 X511 X698 (a, b, c) = (5, 6, 7) | AB = 1

X698 (EVEN (- 4, - 2) 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 \(f(a,b,c) = a ^{-5}(b ^{-2} + c ^{-2}) - a ^{-3}(b ^{-4} + c ^{-4})\)
Barycentrics: \(a^{2} b^{4} + a^{2} c^{4} - b^{4} c^{2} - b^{2} c^{4} : :\)
▸ Incident Central Lines4 lines

{6, 194}, {30, 511}, {75, 257}, {76, 141}

▸ Functional Relations2 relations