X2690

SR(X74, X103)

X2690 = reflection of X2688 in X3
< 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) { 2688, 3 }: Central Line L(2688, 3) { 80, 103 }: Central Line L(80, 103) { 74, 516 }: Central Line L(74, 516) { 101, 523 }: Central Line L(101, 523) { 110, 514 }: Central Line L(110, 514) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2688 = SR(X(74), X(101)) (0.0051, -0.0224) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_80 = REFLECTION OF INCENTER IN FEUERBACH POINT (0.8980, -0.1000) X_103 = ANTIPODE OF X(101) (0.7857, -0.3208) X_74 = ISOGONAL CONJUGATE OF EULER INFINITY POINT (0.7484, -0.3437) X_516 = ISOGONAL CONJUGATE OF X(103) (0.7703, 0.7386) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_514 = ISOGONAL CONJUGATE OF X(101) (1.0761, -0.0329) X_2690 = SR(X(74), X(103)) (0.9949, 0.2266) A B C X2688 X3 X80 X103 X74 X516 X101 X523 X110 X514 X2690 (a, b, c) = (5, 6, 7) | AB = 1

X2690 (SR(X74, X103)) 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) is as given just before X2677 using P = X74, U = X103
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.254969823094\)

X2690 lies on the circumcircle.

▸ Incident Central Lines11 lines

{3, 2688}, {23, 675}, {80, 103}, {74, 516}, {100, 1577}, {101, 523}, {110, 514}, {186, 917}, {551, 953}, {1006, 2687}, {2453, 2758}

▸ Functional Relations5 relations