X916

X103-CEVA CONJUGATE OF X3

As the isogonal conjugate of a point on the circumcircle, X916 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) { 3, 48 }: Central Line L(3, 48) { 72, 185 }: Central Line L(72, 185) { 30, 511 }: Central Line L(30, 511) { 1037, 1069 }: Central Line L(1037, 1069) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_103 = ANTIPODE OF X(101) (0.7857, -0.3208) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5412, 0.1246) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_185 = NAGEL POINT OF THE ORTHIC TRIANGLE (0.6033, 0.1643) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_1037 = CEVAPOINT OF X(55) AND X(56) (0.5823, 0.2853) X_1069 = -CROSS CONJUGATE OF X(3) (0.0709, 0.0059) X_916 = -CEVA CONJUGATE OF X(3) (0.0224, -0.0814) A B C X103 X3 X48 X72 X185 X30 X511 X1037 X1069 X916 (a, b, c) = (5, 6, 7) | AB = 1

X916 (X103-CEVA CONJUGATE OF X3) 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 \(f(a,b,c) = wb^{2} + vc^{2} - a(wb + vc)\),\(u : v : w\) = X4
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

{3, 48}, {30, 511}, {72, 185}, {1037, 1069}

▸ Functional Relations4 relations