X2689

SR(X74, X102)

X2689 = reflection of X2695 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) { 2695, 3 }: Central Line L(2695, 3) { 30, 102 }: Central Line L(30, 102) { 74, 515 }: Central Line L(74, 515) { 109, 523 }: Central Line L(109, 523) { 110, 522 }: Central Line L(110, 522) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2695 = SR(X(74), X(109)) (0.0704, -0.1734) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_102 = Λ(INCENTER, ORTHOCENTER) (0.6364, -0.3897) X_74 = ISOGONAL CONJUGATE OF EULER INFINITY POINT (0.7484, -0.3437) X_515 = ISOGONAL CONJUGATE OF X(102) (0.6804, 0.7691) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_522 = ISOGONAL CONJUGATE OF X(109) (-0.0318, 0.3430) X_2689 = SR(X(74), X(102)) (0.9296, 0.3775) A B C X2695 X3 X30 X102 X74 X515 X109 X523 X110 X522 X2689 (a, b, c) = (5, 6, 7) | AB = 1

X2689 (SR(X74, X102)) 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 = X102
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.648043093795\)

X2689 lies on the circumcircle.

▸ Incident Central Lines8 lines

{3, 2695}, {23, 1311}, {30, 102}, {74, 515}, {109, 523}, {110, 522}, {946, 953}, {1324, 2372}

▸ Functional Relations3 relations