X730

EVEN (- 2, 1) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X730 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) { 10, 39 }: Central Line L(10, 39) { 1, 76 }: Central Line L(1, 76) { 8, 194 }: Central Line L(8, 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_731 = EVEN (- 2, 1) CIRCUMCIRCLE POINT (1.0101, 0.0876) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_1 = INCENTER (0.5714, 0.2333) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_8 = NAGEL POINT (0.4694, 0.1333) 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_730 = EVEN (- 2, 1) INFINITY POINT (0.0843, -0.1730) A B C X731 X10 X39 X1 X76 X8 X194 X30 X511 X730 (a, b, c) = (5, 6, 7) | AB = 1

X730 (EVEN (- 2, 1) 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 \(f(a,b,c) = a ^{-3}(b^{1} + c^{1}) - a^{0}(b ^{-2} + c ^{-2})\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
▸ Incident Central Lines4 lines

{1, 76}, {8, 194}, {10, 39}, {30, 511}

▸ Functional Relations1 relation