At school I used to love the geometry of the circle, but in my own career I had little opportunity to teach it. Now in semi-retirement my work with Teasers in the Sunday Times brings me into contact with many entertaining aspects of mathematics, not least being the occasional piece of geometry. In this short article I will quote four potted versions of recent Teasers, each of which relies on some interesting piece of mathematics, and I shall sketch in each case how that property can be deduced neatly using circles.