Why does tea leave a stain in a cup only in a ring around where the surface of the tea was?

In hard water areas, the water contains quite a lot of calcium in the form of 'temporary hardness' - calcium hydrogen carbonate Ca(HCO3)2. When this is heated, the temporary hardness breaks down into calcium carbonate, which is chalk, and water. These calcium salts can bind to tannins in the tea and form an insoluble precipitate - a scum. These particles float to the top of the tea, and stick to the side of the cup. Tannins contain some of the colour of the tea, and so this ring of particles will be dark, and stain your cup!