X2691

SR(X74, X105)

X2691 = reflection of X2752 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) { 2752, 3 }: Central Line L(2752, 3) { 30, 105 }: Central Line L(30, 105) { 74, 518 }: Central Line L(74, 518) { 523, 1292 }: Central Line L(523, 1292) { 376, 2687 }: Central Line L(376, 2687) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2752 = SR(X(105), X(110)) (0.0184, 0.2709) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_105 = Λ(INCENTER, SYMMEDIAN POINT) (0.9714, -0.0933) X_74 = ISOGONAL CONJUGATE OF EULER INFINITY POINT (0.7484, -0.3437) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9154, 0.6489) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_1292 = COLLINGS TRANSFORM OF X(55) (0.0286, 0.2974) X_376 = CENTROID OF THE ANTIPEDAL TRIANGLE OF X(2) (0.4626, 0.0042) X_2687 = SR(X(74), X(100)) (-0.0092, 0.0687) X_2691 = SR(X(74), X(105)) (0.9816, -0.0668) A B C X2752 X3 X30 X105 X74 X518 X523 X1292 X376 X2687 X2691 (a, b, c) = (5, 6, 7) | AB = 1

X2691 (SR(X74, X105)) 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 = X105
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(3.357130505330\)

X2691 lies on the circumcircle.

▸ Incident Central Lines5 lines

{3, 2752}, {30, 105}, {74, 518}, {376, 2687}, {523, 1292}

▸ Functional Relations2 relations