Aircraft conflict avoidances can be formulated as optimal control problems (the control are the accelerations of the aircraft). Some particular formulations yield convex optimal control problems under some concave inequality constraints including state variables (this is the main difficulty on the resolution of these types of problems). We propose here an original approach combining direct and indirect methods to solve this optimal control problem. This approach is based on the decomposition into zones where the concave inequality constraints could be active and moreover these constraints are proved to be inactive outside. Thus, the problem is then solved by using a direct shooting method inside the zone and, outiside the zone, a solution is analytically provided by directly applying the Pontyagin Maximum Principle. Numerical experiments validated the great efficiency of this approach.