X732

EVEN (- 2, 2) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X732 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, 76 }: Central Line L(6, 76) { 39, 141 }: Central Line L(39, 141) { 69, 194 }: Central Line L(69, 194) { 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_733 = EVEN (- 2, 2) CIRCUMCIRCLE POINT (1.0071, 0.0450) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_141 = COMPLEMENT OF SYMMEDIAN POINT (0.5061, 0.1663) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_194 = -CEVA CONJUGATE OF X(2) (0.6989, 0.3222) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_732 = EVEN (- 2, 2) INFINITY POINT (0.9745, 0.5915) A B C X733 X6 X76 X39 X141 X69 X194 X30 X511 X732 (a, b, c) = (5, 6, 7) | AB = 1

X732 (EVEN (- 2, 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 \(f(a,b,c) = a ^{-3}(b^{2} + c^{2}) - a^{1}(b ^{-2} + c ^{-2})\)
Barycentrics: \((b^{2} + c^{2}) (a^{4} - b^{2} c^{2}) : :\)
▸ Incident Central Lines4 lines

{6, 76}, {30, 511}, {39, 141}, {69, 194}

▸ Functional Relations5 relations