X2709

SR(X98, X111)

X2709 = reflection of X843 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) { 843, 3 }: Central Line L(843, 3) { 111, 352 }: Central Line L(111, 352) { 98, 524 }: Central Line L(98, 524) { 99, 1499 }: Central Line L(99, 1499) { 512, 1296 }: Central Line L(512, 1296) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_843 = ISOGONAL CONJUGATE OF X(543) (0.1427, 0.4664) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_111 = PARRY POINT (0.9885, -0.0457) X_352 = INVERSE-IN-CIRCUMCIRCLE OF X(353) (2.2545, 2.0453) X_98 = TARRY POINT (0.8891, -0.2281) X_524 = ISOGONAL CONJUGATE OF X(111) (0.1376, -0.2297) X_99 = STEINER POINT (0.1109, 0.4322) X_1499 = POINT BIHAM (0.1078, 0.5997) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0394, -0.1040) X_1296 = COLLINGS TRANSFORM OF X(126) (0.0115, 0.2498) X_2709 = SR(X(98), X(111)) (0.8573, -0.2623) A B C X843 X3 X111 X352 X98 X524 X99 X1499 X512 X1296 X2709 (a, b, c) = (5, 6, 7) | AB = 1

X2709 (SR(X98, X111)) 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 \(f(a,b,c) = a/[(b^{2} - c^{2})(4a^{4} + b^{4} + c^{4} - a^{2}b^{2} - a^{2}c^{2} - 4b^{2}c^{2})]\) (M. Iliev, 5/13/07)
Search Value (6, 9, 13): \(8.496827900003\)

X2709 lies on the circumcircle.

▸ Incident Central Lines8 lines

{3, 843}, {98, 524}, {99, 1499}, {111, 352}, {512, 1296}, {691, 2421}, {729, 2080}, {842, 1350}

▸ Functional Relations5 relations