X2758

SR(X106, X110)

X2768 = reflection of X2692 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) { 2692, 3 }: Central Line L(2692, 3) { 106, 523 }: Central Line L(106, 523) { 110, 519 }: Central Line L(110, 519) { 10, 901 }: Central Line L(10, 901) { 30, 1293 }: Central Line L(30, 1293) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2692 = SR(X(74), X(106)) (0.9406, -0.1554) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_106 = Λ(INCENTER, CENTROID) (1.0000, 0.0000) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_901 = ISOGONAL CONJUGATE OF X(900) (1.0000, -0.0000) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_1293 = COLLINGS TRANSFORM OF X(121) (0.0000, 0.2041) X_2758 = SR(X(106), X(110)) (0.0594, 0.3595) A B C X2692 X3 X106 X523 X110 X519 X10 X901 X30 X1293 X2758 (a, b, c) = (5, 6, 7) | AB = 1

X2758 (SR(X106, X110)) 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 = X110
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(7.006542116291\)

X2758 lies on the circumcircle.

▸ Incident Central Lines7 lines

{3, 2692}, {10, 901}, {30, 1293}, {106, 523}, {110, 519}, {404, 1290}, {2453, 2690}

▸ Functional Relations6 relations