In this paper, we consider a pursuit-evasion game problem in a geometric setting, where a single pursuer and single evader are in motion with conflicting interests. The pursuer follows a recently introduced angular acceleration guidance law to catch the evader and the evader-centric strategy is supposed to keep the evader away from the pursuer for maximum possible time in an unknown environment having static obstacles. An evader-centric approach is proposed in the present paper that uses linear extrapolation to predict the future move of the evader and define its own strategy. The well-known tangent bug algorithm is employed to deal with static obstacles. Effectiveness of the proposed evader's strategy has been analyzed in terms of interception time and distance travelled by the players. Simulation results demonstrate effectiveness and efficiency of the proposed method.