I think H. S. M. Coxeter's books are good sources for training in geometry, leading to ideas in groups. I haven't looked at this book by Stillwell, so I am not

I think H. S. M. Coxeter's books are good sources for training in geometry, leading to ideas in groups. I haven't looked at this book by Stillwell, so I am not aware of the difficulty of problems presented in this book. There is an old Schaum's series book on Projective Geometry that was very useful to get the basic ideas quickly. It may not be an elegant presentation of the subject, but it was very quick, and to the point. All said and done, synthetic geometry (not analytic geometry) is not very easy, and it might help to create models (wire-frame or 3d cardboard or plasticine/play-dough) to visualize things. They may not help to solve the problem rigorously, however. By coincidence, I am slowly working through another of Stillwell's books, on Reverse Mathematics. You are right, his way of presenting things suddenly makes things you know snap into place.