X2727

SR(X101, X107)

X2727 = reflection of X2738 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) { 2738, 3 }: Central Line L(2738, 3) { 101, 520 }: Central Line L(101, 520) { 107, 514 }: Central Line L(107, 514) { 112, 1459 }: Central Line L(112, 1459) { 516, 1294 }: Central Line L(516, 1294) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2738 = SR(X(103), X(107)) (0.1824, -0.2974) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_520 = ISOGONAL CONJUGATE OF X(107) (-0.0490, 0.2227) X_107 = Ψ(SYMMEDIAN POINT, ORTHOCENTER) (0.5733, 0.6071) X_514 = ISOGONAL CONJUGATE OF X(101) (1.0761, -0.0329) X_112 = Ψ(ORTHOCENTER, SYMMEDIAN POINT) (0.5162, 0.6121) X_1459 = -BETH CONJUGATE OF X(521) (3.6667, -0.5443) X_516 = ISOGONAL CONJUGATE OF X(103) (0.7703, 0.7386) X_1294 = COLLINGS TRANSFORM OF X(122) (0.4267, -0.4030) X_2727 = SR(X(101), X(107)) (0.8176, 0.5015) A B C X2738 X3 X101 X520 X107 X514 X112 X1459 X516 X1294 X2727 (a, b, c) = (5, 6, 7) | AB = 1

X2727 (SR(X101, X107)) 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 = X101, U = X107
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.223546091818\)

X2727 lies on the circumcircle.

▸ Incident Central Lines6 lines

{3, 2738}, {101, 520}, {107, 514}, {112, 1459}, {516, 1294}, {946, 2723}

▸ Functional Relations2 relations