X2757

SR(X106, X109)

X2757 = reflection of X2731 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) { 2731, 3 }: Central Line L(2731, 3) { 106, 522 }: Central Line L(106, 522) { 109, 519 }: Central Line L(109, 519) { 8, 901 }: Central Line L(8, 901) { 515, 1293 }: Central Line L(515, 1293) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2731 = SR(X(102), X(106)) (0.9889, -0.0443) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_106 = Λ(INCENTER, CENTROID) (1.0000, 0.0000) X_522 = ISOGONAL CONJUGATE OF X(109) (-0.0318, 0.3430) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_8 = NAGEL POINT (0.4694, 0.1333) X_901 = ISOGONAL CONJUGATE OF X(900) (1.0000, -0.0000) X_515 = ISOGONAL CONJUGATE OF X(102) (0.6804, 0.7691) X_1293 = COLLINGS TRANSFORM OF X(121) (0.0000, 0.2041) X_2757 = SR(X(106), X(109)) (0.0111, 0.2484) A B C X2731 X3 X106 X522 X109 X519 X8 X901 X515 X1293 X2757 (a, b, c) = (5, 6, 7) | AB = 1

X2757 (SR(X106, 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 = X106, U = X109
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(8.397134448175\)

X2757 lies on the circumcircle.

▸ Incident Central Lines6 lines

{3, 2731}, {8, 901}, {101, 2325}, {106, 522}, {109, 519}, {515, 1293}

▸ Functional Relations2 relations