X2697

SR(X74, X112)

X2697 = reflection of X935 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) { 935, 3 }: Central Line L(935, 3) { 23, 107 }: Central Line L(23, 107) { 30, 112 }: Central Line L(30, 112) { 22, 476 }: Central Line L(22, 476) { 74, 525 }: Central Line L(74, 525) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_935 = POINT ALCOR (0.8281, 0.4929) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_23 = FAR-OUT POINT (1.3871, 2.4232) X_107 = Ψ(SYMMEDIAN POINT, ORTHOCENTER) (0.5733, 0.6071) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_112 = Ψ(ORTHOCENTER, SYMMEDIAN POINT) (0.5162, 0.6121) X_22 = EXETER POINT (0.4143, -0.1221) X_476 = TIXIER POINT (0.9824, 0.2685) X_74 = ISOGONAL CONJUGATE OF EULER INFINITY POINT (0.7484, -0.3437) X_525 = ISOGONAL CONJUGATE OF X(112) (-0.0468, 0.2556) X_2697 = SR(X(74), X(112)) (0.1719, -0.2888) A B C X935 X3 X23 X107 X30 X112 X22 X476 X74 X525 X2697 (a, b, c) = (5, 6, 7) | AB = 1

X2697 (SR(X74, X112)) 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 = X74, U = X112
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(12.355855489710\)

X2697 lies on the circumcircle.

▸ Incident Central Lines14 lines

{2, 1304}, {3, 935}, {20, 691}, {22, 476}, {23, 107}, {30, 112}, {74, 525}, {99, 1236}, {110, 858}, {186, 1289}, {468, 1301}, {523, 1297}, {827, 3153}, {850, 2373}

▸ Functional Relations3 relations