The purple circle with center O and radius R lies inside the red angle at V. Find the blue circle that touches both sides of the angle and the purple circle.
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.