The aircraft collision detection and resolution problem in air traffic management by turn change maneuvers is presented. A two-step approach is presented. The first step consists of a nonconvex Mixed Integer Nonlinear Optimization (MINLO) model based on geometric constructions. The second step consists of a set of quadratic optimization models where aircraft are forced to return to their original flight plan as soon as possible once there is no aircraft in conflict. The main results of extensive computation are reported by comparing the performance of state-of-the-art nonconvex MINLO solvers and an approximation by discretizing the possible angles of motion for solving a Sequence of Integer Linear Optimization (SILO) models in an iterative way. Minotaur, one of the nonconvex MINLO solvers experimented with, gives better solutions but requires more computing time than the SILO approach. However, the latter requires only a short time to obtain a good feasible solution. Its value in the objective function has a reasonable goodness gap from the Minotaur solution.