X2770

SR(X110, X111)

X2770 = reflection of X2696 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) { 2696, 3 }: Central Line L(2696, 3) { 23, 99 }: Central Line L(23, 99) { 112, 468 }: Central Line L(112, 468) { 110, 524 }: Central Line L(110, 524) { 111, 523 }: Central Line L(111, 523) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2696 = SR(X(74), X(111)) (0.9625, -0.1136) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_23 = FAR-OUT POINT (1.3871, 2.4232) X_99 = STEINER POINT (0.1109, 0.4322) X_112 = Ψ(ORTHOCENTER, SYMMEDIAN POINT) (0.5162, 0.6121) X_468 = -LINE CONJUGATE OF X(3) (0.7498, 0.7558) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_524 = ISOGONAL CONJUGATE OF X(111) (0.1376, -0.2297) X_111 = PARRY POINT (0.9885, -0.0457) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_2770 = SR(X(110), X(111)) (0.0375, 0.3178) A B C X2696 X3 X23 X99 X112 X468 X110 X524 X111 X523 X2770 (a, b, c) = (5, 6, 7) | AB = 1

X2770 (SR(X110, X111)) 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 = X110, U = X111
Barycentrics: \(1/(b^{6} + c^{6} - a^{4} b^{2} - a^{4} c^{2} + 4 a^{2} b^{2} c^{2} - 2 b^{4} c^{2} - 2 b^{2} c^{4}) : :\)
Search Value (6, 9, 13): \(8.352436801384\)

X2770 lies on the circumcircle.

▸ Incident Central Lines10 lines

{2, 691}, {3, 2696}, {23, 99}, {25, 935}, {30, 1296}, {74, 1499}, {110, 524}, {111, 523}, {112, 468}, {476, 1995}

▸ Functional Relations6 relations