X2762

SR(X107, X109)

X2762 = reflection of X2732 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) { 2732, 3 }: Central Line L(2732, 3) { 107, 522 }: Central Line L(107, 522) { 109, 520 }: Central Line L(109, 520) { 108, 656 }: Central Line L(108, 656) { 112, 652 }: Central Line L(112, 652) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2732 = SR(X(102), X(107)) (0.3259, -0.3776) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_107 = Ψ(SYMMEDIAN POINT, ORTHOCENTER) (0.5733, 0.6071) X_522 = ISOGONAL CONJUGATE OF X(109) (-0.0318, 0.3430) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_520 = ISOGONAL CONJUGATE OF X(107) (-0.0490, 0.2227) X_108 = Ψ(CIRCUMCENTER, INCENTER) (0.5320, 0.6114) X_656 = CROSSDIFFERENCE OF X(1) AND X(19) (7.5714, -0.8554) X_112 = Ψ(ORTHOCENTER, SYMMEDIAN POINT) (0.5162, 0.6121) X_652 = CROSSDIFFERENCE OF X(1) AND X(4) (7.2558, -0.6836) X_2762 = SR(X(107), X(109)) (0.6741, 0.5818) A B C X2732 X3 X107 X522 X109 X520 X108 X656 X112 X652 X2762 (a, b, c) = (5, 6, 7) | AB = 1

X2762 (SR(X107, X109)) 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 = X107, U = X109
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(1.413798766908\)

X2762 lies on the circumcircle.

▸ Incident Central Lines6 lines

{3, 2732}, {107, 522}, {108, 656}, {109, 520}, {112, 652}, {515, 1294}

▸ Functional Relations2 relations