X2766

SR(X108, X110)

X2766 = reflection of X2694 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) { 2694, 3 }: Central Line L(2694, 3) { 104, 186 }: Central Line L(104, 186) { 105, 468 }: Central Line L(105, 468) { 108, 523 }: Central Line L(108, 523) { 110, 521 }: Central Line L(110, 521) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2694 = SR(X(74), X(108)) (0.1842, -0.2988) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_104 = ANTIPODE OF X(100) (0.8571, -0.2624) X_186 = INVERSE-IN-CIRCUMCIRCLE OF X(4) (0.7957, 0.8758) X_105 = Λ(INCENTER, SYMMEDIAN POINT) (0.9714, -0.0933) X_468 = -LINE CONJUGATE OF X(3) (0.7498, 0.7558) X_108 = Ψ(CIRCUMCENTER, INCENTER) (0.5320, 0.6114) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_521 = ISOGONAL CONJUGATE OF X(108) (1.1224, 0.1534) X_2766 = SR(X(108), X(110)) (0.8158, 0.5029) A B C X2694 X3 X104 X186 X105 X468 X108 X523 X110 X521 X2766 (a, b, c) = (5, 6, 7) | AB = 1

X2766 (SR(X108, 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 = X108, U = X110
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.995652886267\)

X2766 lies on the circumcircle.

▸ Incident Central Lines12 lines

{3, 2694}, {4, 2687}, {25, 2752}, {30, 1295}, {104, 186}, {105, 468}, {108, 523}, {109, 656}, {110, 521}, {112, 650}, {403, 915}, {759, 2074}

▸ Functional Relations5 relations