X2712

SR(X99, X106)

X2712 = reflection of X2705 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) { 2705, 3 }: Central Line L(2705, 3) { 101, 187 }: Central Line L(101, 187) { 99, 519 }: Central Line L(99, 519) { 106, 512 }: Central Line L(106, 512) { 58, 691 }: Central Line L(58, 691) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2705 = SR(X(98), X(106)) (0.8222, -0.2937) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_187 = INVERSE-IN-CIRCUMCIRCLE OF X(6) (SCHOUTE CENTER) (1.1986, 1.2559) X_99 = STEINER POINT (0.1109, 0.4322) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_106 = Λ(INCENTER, CENTROID) (1.0000, 0.0000) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0394, -0.1040) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_691 = TRILINEAR POLE OF LINE X(6)X(110) (1.0101, 0.0886) X_2712 = SR(X(99), X(106)) (0.1778, 0.4978) A B C X2705 X3 X101 X187 X99 X519 X106 X512 X58 X691 X2712 (a, b, c) = (5, 6, 7) | AB = 1

X2712 (SR(X99, 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) is as given just before X2677 using P = X99, U = X106
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(3.782871270416\)

X2712 lies on the circumcircle.

▸ Incident Central Lines11 lines

{3, 2705}, {6, 2702}, {42, 901}, {58, 691}, {99, 519}, {100, 896}, {101, 187}, {106, 512}, {110, 902}, {111, 649}, {511, 1293}

▸ Functional Relations3 relations