X1912

IDEAL POINT OF PU(9)

As the isogonal conjugate of a point on the circumcircle, X1912 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) { 30, 511 }: Central Line L(30, 511) { 213, 667 }: Central Line L(213, 667) { 1166, 1203 }: Central Line L(1166, 1203) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_213 = -CEVA CONJUGATE OF X(42) (0.6135, 0.2833) X_667 = CROSSDIFFERENCE OF X(2) AND X(37) (-6.1667, 5.7155) X_1166 = 1st SARAGOSSA POINT OF X(5) (0.6183, 0.2746) X_1203 = 3rd SARAGOSSA POINT OF X(58) (0.6034, 0.2712) X_1912 = IDEAL POINT OF PU(9) (0.0794, 0.5669) A B C X30 X511 X213 X667 X1166 X1203 X1912 (a, b, c) = (5, 6, 7) | AB = 1

X1912 (IDEAL POINT OF PU(9)) 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 \(f(a,b,c) = b - c - a(b/c + c/b)(b/c - c/b)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
▸ Incident Central Lines3 lines

{30, 511}, {213, 667}, {1166, 1203}

▸ Functional Relations1 relation