X2731

SR(X102, X106)

X2731 = reflection of X2757 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) { 2757, 3 }: Central Line L(2757, 3) { 102, 519 }: Central Line L(102, 519) { 106, 515 }: Central Line L(106, 515) { 522, 1293 }: Central Line L(522, 1293) { 944, 953 }: Central Line L(944, 953) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2757 = SR(X(106), X(109)) (0.0111, 0.2484) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_102 = Λ(INCENTER, ORTHOCENTER) (0.6364, -0.3897) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_106 = Λ(INCENTER, CENTROID) (1.0000, 0.0000) X_515 = ISOGONAL CONJUGATE OF X(102) (0.6804, 0.7691) X_522 = ISOGONAL CONJUGATE OF X(109) (-0.0318, 0.3430) X_1293 = COLLINGS TRANSFORM OF X(121) (0.0000, 0.2041) X_944 = HOFSTADTER TRAPEZOID POINT (0.5306, 0.0708) X_953 = ISOGONAL CONJUGATE OF X(952) (0.0000, 0.2041) X_2731 = SR(X(102), X(106)) (0.9889, -0.0443) A B C X2757 X3 X102 X519 X106 X515 X522 X1293 X944 X953 X2731 (a, b, c) = (5, 6, 7) | AB = 1

X2731 (SR(X102, X106)) 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 = X102, U = X106
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(5.167591340217\)

X2731 lies on the circumcircle.

▸ Incident Central Lines6 lines

{3, 2757}, {102, 519}, {106, 515}, {243, 2376}, {522, 1293}, {944, 953}

▸ Functional Relations2 relations