X726

EVEN (- 2, -1) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X726 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) { 37, 39 }: Central Line L(37, 39) { 10, 75 }: Central Line L(10, 75) { 1, 87 }: Central Line L(1, 87) { 38, 321 }: Central Line L(38, 321) { 190, 238 }: Central Line L(190, 238) { 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_727 = EVEN (- 2, -1) CIRCUMCIRCLE POINT (1.0060, 0.1685) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_1 = INCENTER (0.5714, 0.2333) X_87 = -CROSS CONJUGATE OF X(1) (0.4794, 0.1691) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_321 = ISOTOMIC CONJUGATE OF X(81) (0.4800, 0.1527) X_190 = YFF PARABOLIC POINT (0.0748, 0.3999) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_726 = EVEN (- 2, -1) INFINITY POINT (1.0187, 0.5358) A B C X727 X37 X39 X10 X75 X1 X87 X38 X321 X190 X238 X30 X511 X726 (a, b, c) = (5, 6, 7) | AB = 1

X726 (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 \(f(a,b,c) = a ^{-3}(b ^{-1} + c ^{-1}) - a ^{-2}(b ^{-2} + c ^{-2})\)
Barycentrics: \(a (b^{2} + c^{2}) - b c (b + c) : :\)
▸ Incident Central Lines8 lines

{1, 87}, {10, 75}, {30, 511}, {37, 39}, {38, 321}, {190, 238}, {291, 350}, {312, 982}

▸ Functional Relations4 relations