Three circles are given: a around A with radius r, the smallest, b around B and c around C. Find the circle that encloses all three and touches each of them: one of the eight circles touching three given circles, Apollonius's problem, and the longest construction in the gallery.
The source code is at github.com/KirillOsenkov/LiveGeometry. It is written in .NET and Avalonia.
Also here: Catriona Agg's geometry puzzles made interactive; the same gallery in plain JavaScript; and how to embed a live drawing in your own page.