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In this paper, the problem of localizing and circumnavigating an unknown stationary target by multiple autonomous agents using bearing-only measurements is studied. We assume that all agents are anonymous in the sense that they are indistinguishable from each other, and each agent is not permitted to exchange its local measurements or state information. A novel collision avoidance mechanism is proposed to ensure collision-free system evolution, and a distributed control algorithm is developed to steer the group of agents to circumnavigate the target at a desired distance with any prescribed angular spaced formation. Global finite-time stability of the system is rigorously derived. The performance of the proposed algorithms is verified through numerical simulations. [ABSTRACT FROM AUTHOR]