X2752

SR(X105, X110)

X2752 = reflection of X2691 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) { 2691, 3 }: Central Line L(2691, 3) { 23, 100 }: Central Line L(23, 100) { 108, 468 }: Central Line L(108, 468) { 105, 523 }: Central Line L(105, 523) { 110, 518 }: Central Line L(110, 518) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2691 = SR(X(74), X(105)) (0.9816, -0.0668) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_23 = FAR-OUT POINT (1.3871, 2.4232) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_108 = Ψ(CIRCUMCENTER, INCENTER) (0.5320, 0.6114) X_468 = -LINE CONJUGATE OF X(3) (0.7498, 0.7558) X_105 = Λ(INCENTER, SYMMEDIAN POINT) (0.9714, -0.0933) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9154, 0.6489) X_2752 = SR(X(105), X(110)) (0.0184, 0.2709) A B C X2691 X3 X23 X100 X108 X468 X105 X523 X110 X518 X2752 (a, b, c) = (5, 6, 7) | AB = 1

X2752 (SR(X105, X110)) 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 = X105, U = X110
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(10.207595283063\)

X2752 lies on the circumcircle.

▸ Incident Central Lines17 lines

{2, 1290}, {3, 2691}, {21, 691}, {23, 100}, {25, 2766}, {28, 935}, {80, 1292}, {37, 919}, {99, 1325}, {105, 523}, {108, 468}, {109, 896}, {110, 518}, {111, 650}, {112, 2074}, {927, 1441}, {1083, 2703}

▸ Functional Relations4 relations