In this paper, we address a visibility-based target tracking game for the scenario when the environment contains a circular obstacle. The game is originally formulated in four dimensions, but due to the symmetry of the environment, the dimension of the state space can be reduced to three. In the reduced state space, we formulate a game of degree. We use Isaacs techniques to obtain the locally optimal solution of the players. These solutions are extended back in the state space keeping in mind the geometry of the environment to obtain complete solution in the solution. Finally, we construct vector fields whose integral curves are the optimal solutions in the state space.

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