I've recently been introduced to inversive geometry. This seems like it would be a very pretty area of study. Many sources that I have found seem a little old, however. I have two related questions:
The wiki page (linked above) suggests that there are various problems in geometry which are known to be solvable using inversive geometry. What are examples of these? I have found one very exciting one explained by Numberphile here. Are there more?
My looking around in various places suggests that inversive geometry is not such an active area of research at the moment. Is this true? Has it been superseded by other geometries, i.e. projective geometry?
Are there any authoritative books on inversive geometry, or any in particular which are known to be a good introduction to the subject?