The market of Unmanned Aerial Vehicles (UAVs) for civil applications is extensively growing. Indeed, these airplanes are now widely used in applications such as data gathering, agriculture monitoring and rescue. The UAVs are required to track a fixed or moving object; thus, tracking control algorithms that ensure the system stability and that have a quick time response must be developed. This paper tackles the problem of supervising a fixed target using a fixed wing UAV flying at a constant altitude and a constant speed. For that purpose, three control algorithms were developed. In all of the algorithms, the UAV is expected to hover around the target in a circular trajectory. Moreover, the three approaches are based upon a Lyapunov-LaSalle stabilization method. The first tracking algorithm ensures that the UAV circles around the target. However, the path that the UAV follows in order to join this pattern is not studied. In the second and third approach, two different techniques that allow the UAV to intercept its final circular pattern in the quickest possible time and thus follow the tangent to the circular pattern are presented. Simulation results that show and compare the performances of the proposed methods are presented.