X2717

SR(X100, X103)

X2717 = reflection of X1308 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) { 1308, 3 }: Central Line L(1308, 3) { 100, 516 }: Central Line L(100, 516) { 103, 513 }: Central Line L(103, 513) { 101, 517 }: Central Line L(101, 517) { 104, 514 }: Central Line L(104, 514) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1308 = COLLINGS TRANSFORM OF X(661) (1.0102, 0.0916) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_516 = ISOGONAL CONJUGATE OF X(103) (0.7703, 0.7386) X_103 = ANTIPODE OF X(101) (0.7857, -0.3208) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8180, 0.7154) X_104 = ANTIPODE OF X(100) (0.8571, -0.2624) X_514 = ISOGONAL CONJUGATE OF X(101) (1.0761, -0.0329) X_2717 = SR(X(100), X(103)) (-0.0102, 0.1125) A B C X1308 X3 X100 X516 X103 X513 X101 X517 X104 X514 X2717 (a, b, c) = (5, 6, 7) | AB = 1

X2717 (SR(X100, X103)) 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 = X100, U = X103
Search Value (6, 9, 13): \(14.198476839870\)

X2717 lies on the circumcircle.

▸ Incident Central Lines16 lines

{3, 1308}, {36, 934}, {40, 2742}, {55, 2222}, {57, 2720}, {92, 1309}, {100, 516}, {101, 517}, {103, 513}, {104, 514}, {108, 2078}, {109, 1155}, {165, 901}, {573, 813}, {650, 2291}, {1292, 2077}

▸ Functional Relations4 relations

Notes

Let JaJbJc be the excentral triangle. Let La be the line X115X125 of the triangle JaBC, and define Lb and Lc cyclically. Let A″ = Lb∩Lc, and define B″ and C″ cyclically. Then A″B″C″ is perspective to ABC, and the perspector is X2717. (Randy Hutson, July 31 2018)