X2693

SR(X74, X107)

X2693 = reflection of X1304 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) { 1304, 3 }: Central Line L(1304, 3) { 30, 107 }: Central Line L(30, 107) { 20, 476 }: Central Line L(20, 476) { 74, 520 }: Central Line L(74, 520) { 376, 935 }: Central Line L(376, 935) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1304 = COLLINGS TRANSFORM OF X(403) (0.7822, 0.5273) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_107 = Ψ(SYMMEDIAN POINT, ORTHOCENTER) (0.5733, 0.6071) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_476 = TIXIER POINT (0.9824, 0.2685) X_74 = ISOGONAL CONJUGATE OF EULER INFINITY POINT (0.7484, -0.3437) X_520 = ISOGONAL CONJUGATE OF X(107) (-0.0490, 0.2227) X_376 = CENTROID OF THE ANTIPEDAL TRIANGLE OF X(2) (0.4626, 0.0042) X_935 = POINT ALCOR (0.8281, 0.4929) X_2693 = SR(X(74), X(107)) (0.2178, -0.3231) A B C X1304 X3 X30 X107 X20 X476 X74 X520 X376 X935 X2693 (a, b, c) = (5, 6, 7) | AB = 1

X2693 (SR(X74, X107)) 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 = X107
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(13.017650887597\)

X2693 lies on the circumcircle.

▸ Incident Central Lines10 lines

{3, 1304}, {20, 476}, {30, 107}, {74, 520}, {110, 2071}, {186, 1301}, {376, 935}, {523, 1294}, {673, 2481}, {858, 1302}

▸ Functional Relations5 relations