Minimum circle circumnavigation is proposed in this paper, which is of special value in target monitoring, capturing and/or attacking. With this new pattern, our goal is to steer one agent to enclose multiple targets along a safe and minimum circular orbit with the desired tangential speed. This is achieved by a control protocol with dynamic compensators, which is also capable of avoiding collision between the agent and the multiple targets during the whole operational process. The control protocol is further extended to the scenarios of multiple agents circulating a group of targets by adding a coordination mechanism into the tangential velocity term, which allows the agents to distribute evenly on each expected circular orbit with the same or different radius. Simulations results illustrate the effectiveness of the proposed methods.