% !TEX TS-program = lualatex % Created by Alain Matthes on 2024-12-25. % Copyright (c) 2024 AlterMundus. \documentclass[margin = 12pt]{standalone} \usepackage[mini]{tkz-euclide} \usepackage{tkz-elements} \begin{document} % The Feuerbach triangle is the triangle formed by the three points of tangency of the nine-point circle with the excircles \directlua{ z.A = point(0, 0) z.B = point(6, 0) z.C = point(0.8, 4) T.ABC = triangle(z.A, z.B, z.C) z.N = T.ABC.eulercenter z.S = T.ABC.spiekercenter T.feuerbach = T.ABC:feuerbach() z.Ea, z.Eb, z.Ec = T.feuerbach:get() T.excentral = T.ABC:excentral() z.Ja, z.Jb, z.Jc = T.excentral:get() C.JaEa = circle:new(z.Ja, z.Ea) % C.ortho = circle:radius(z.S, math.sqrt(C.JaEa:power(z.S))) C.ortho = C.JaEa:orthogonal_from(z.S) z.a = C.ortho.through C.euler = T.ABC:euler_circle() C.apo = C.ortho:inversion(C.euler) z.O = C.apo.center z.xa, z.xb, z.xc = C.ortho:inversion(z.Ea, z.Eb, z.Ec) } \begin{tikzpicture}[ scale = .6] \tkzGetNodes \tkzFillCircles[green!30](O,xa) \tkzFillCircles[teal!30](Ja,Ea Jb,Eb Jc,Ec) \tkzFillCircles[lightgray](S,a) \tkzFillCircles[green!30](N,Ea) \tkzDrawPoints(xa,xb,xc) \tkzClipCircle(O,xa) \tkzDrawLines[add=3 and 3](A,B A,C B,C) \tkzDrawCircles(Ja,Ea Jb,Eb Jc,Ec S,a O,xa N,Ea) \tkzDrawPoints(O,A,B,C,S,Ea,Eb,Ec,N) \tkzDrawSegments[dashed](S,xa S,xb S,xc) \tkzLabelPoints(O,N,A,B) \tkzLabelPoints[right](S,C) \end{tikzpicture} \end{document}