More on Wilson loops for two touching circles

We calculate both at leading weak and strong coupling the renormalised Maldacena-Wilson loop for contours formed by consecutive passage of two touching circles. At the touching point both circles should have the same normal direction but form cusps of non-zero opening angle $\alpha$. Particular emphasis is put on the behaviour in the limit $\alpha\rightarrow 0$ and its comparison with the spiky situation studied in a previous paper, where $\alpha$ was set to zero before renormalisation.