X2718

SR(X100, X106)

X2718 = X2265-cross conjugate of X57
< 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) { 2743, 3 }: Central Line L(2743, 3) { 36, 100 }: Central Line L(36, 100) { 44, 101 }: Central Line L(44, 101) { 106, 513 }: Central Line L(106, 513) { 1, 901 }: Central Line L(1, 901) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2743 = SR(X(104), X(106)) (0.8571, -0.2624) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_106 = Λ(INCENTER, CENTROID) (1.0000, 0.0000) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_1 = INCENTER (0.5714, 0.2333) X_901 = ISOGONAL CONJUGATE OF X(900) (1.0000, -0.0000) X_2718 = SR(X(100), X(106)) (0.1429, 0.4666) A B C X2743 X3 X36 X100 X44 X101 X106 X513 X1 X901 X2718 (a, b, c) = (5, 6, 7) | AB = 1

X2718 (SR(X100, 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 \(f(a,b,c) = 1/(b^{3} + c^{3} - a^{2}b - a^{2}c - 2b^{2}c - 2bc^{2} + 4abc)\) (M. Iliev, 5/13/07)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(4.695525551814\)

X2718 lies on the circumcircle.

▸ Incident Central Lines15 lines

{1, 901}, {3, 2743}, {36, 100}, {44, 101}, {56, 2222}, {106, 513}, {108, 1877}, {109, 1319}, {214, 765}, {244, 1168}, {517, 1293}, {609, 919}, {898, 993}, {999, 1308}, {1420, 2720}

▸ Functional Relations9 relations