let $f$ be an open family of circles in the complex plane and let $p$ be the union of all the circles from $f$. suppose that $f$ is a continuous function on $p$ which extends holomorphically from each circle $c$ belonging to $f$ (that is, its restriction to $c$ extends holomorphically through the disc bounded by $c$). is $f$ holomorphic on $p$? we show that this question is naturally related to a question in $c^2$ and then, for certain families $f$, we show how some standard facts from several complex variables can be used to deal with this question.