X2723

SR(X101, X102)

X2723 = reflection of X929 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) { 929, 3 }: Central Line L(929, 3) { 108, 243 }: Central Line L(108, 243) { 101, 515 }: Central Line L(101, 515) { 102, 514 }: Central Line L(102, 514) { 103, 522 }: Central Line L(103, 522) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_929 = ISOGONAL CONJUGATE OF X(928) (0.9516, 0.3396) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_108 = Ψ(CIRCUMCENTER, INCENTER) (0.5320, 0.6114) X_243 = -LINE CONJUGATE OF X(73) (0.7516, 0.9505) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_515 = ISOGONAL CONJUGATE OF X(102) (0.6804, 0.7691) X_102 = Λ(INCENTER, ORTHOCENTER) (0.6364, -0.3897) X_514 = ISOGONAL CONJUGATE OF X(101) (1.0761, -0.0329) X_103 = ANTIPODE OF X(101) (0.7857, -0.3208) X_522 = ISOGONAL CONJUGATE OF X(109) (-0.0318, 0.3430) X_2723 = SR(X(101), X(102)) (0.0484, -0.1355) A B C X929 X3 X108 X243 X101 X515 X102 X514 X103 X522 X2723 (a, b, c) = (5, 6, 7) | AB = 1

X2723 (SR(X101, 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 = X101, U = X102
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(13.253772930915\)

X2723 lies on the circumcircle.

▸ Incident Central Lines10 lines

{3, 929}, {101, 515}, {102, 514}, {103, 522}, {108, 243}, {109, 516}, {497, 2720}, {813, 1766}, {946, 2727}, {1021, 2249}

▸ Functional Relations2 relations