X2734

SR(X102, X109)

X2734 = reflection of X1309 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) { 1309, 3 }: Central Line L(1309, 3) { 102, 522 }: Central Line L(102, 522) { 109, 515 }: Central Line L(109, 515) { 20, 901 }: Central Line L(20, 901) { 107, 859 }: Central Line L(107, 859) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1309 = COLLINGS TRANSFORM OF X(860) (0.4052, -0.3994) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_102 = Λ(INCENTER, ORTHOCENTER) (0.6364, -0.3897) X_522 = ISOGONAL CONJUGATE OF X(109) (-0.0318, 0.3430) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_515 = ISOGONAL CONJUGATE OF X(102) (0.6804, 0.7691) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_901 = ISOGONAL CONJUGATE OF X(900) (1.0000, -0.0000) X_107 = Ψ(SYMMEDIAN POINT, ORTHOCENTER) (0.5733, 0.6071) X_859 = INTERCEPT OF EULER LINE AND TRILINEAR POLAR OF X(81) (1.1279, 1.7448) X_2734 = SR(X(102), X(109)) (0.4480, -0.1728) A B C X1309 X3 X102 X522 X109 X515 X20 X901 X107 X859 X2734 (a, b, c) = (5, 6, 7) | AB = 1

X2734 (SR(X102, 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 = X102, U = X109
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(12.023047806100\)

X2734 lies on the circumcircle.

▸ Incident Central Lines6 lines

{3, 1309}, {20, 901}, {102, 522}, {107, 859}, {109, 515}, {944, 2720}

▸ Functional Relations3 relations