A target-attacker-defender (TAD) game is a fascinating differential game in both nature and the artificial world. This article considers a TAD game with a nonsuicidal faster attacker that aims to capture the target while avoiding being captured by the defender. The attacker is both a pursuer (pursues the target) and an evader (evades the defender). Naturally, one wonders when and how the attacker can chase the target and when and how the attacker can evade the defender. In this article, we first analyze the possibility of winning the game for the attacker under the framework of games of kind. Then, we present three different stages and corresponding control strategies, as well as the conditions for switching stages. In addition, the target cooperates with the defender to compose a team as the opponent of the attacker. Different capture radii also affect cooperation between the target and defender. When the capture radius of the defender is less than that of the attacker, the target and defender cooperate to avoid being captured by the attacker or to extend the time to be captured. Conversely, when the capture radius of the attacker is less than that of the defender, the target-defender team can adopt a rendezvous strategy to end the engagement. We derive the initial state under which the target can rendezvous with the defender before the target is captured by the attacker.