Proceedings of the Edinburgh Mathematical Society

Research Article

On the Number and Nature of the Solutions of the Apollonian Contact Problem

R. F. Muirhead

The problem of describing a circle to touch three circles, including the nine special cases when one or more of the radii of the given circles are zero or infinite, was solved by Apollonius of Perga in a work which was lost, but of which Pappus has given some account in his Mathematical Collections. Towards the end of the l6th century the problem was again taken up and solved by F. Vieta, and since that time it has formed the subject of investigations by many mathematicians, from many different points of view.