This work employs an unmanned aerial vehicle (UAV) as a jammer to aid a covert communication from a transmitter Alice to a receiver Bob, where the UAV transmits artificial noise (AN) with random power to deliberately create interference to a warden Willie. In the considered system, the UAV's trajectory is critical to the covert communication performance, since the AN transmitted by the UAV also generates interference to Bob. To maximize the system performance, we formulate an optimization problem to jointly design the UAV's trajectory and Alice's transmit power. The formulated optimization problem is non-convex and is normally solved by a conventional iterative (CI) method, which requires multiple approximations based on Taylor expansions and an initialization on the UAV's trajectory. In order to eliminate these requirements, this work, for the first time, develops a geometric (GM) method to solve the optimization problem. By analyzing the covertness constraint, the GM method decouples the joint optimization into optimizing the UAV's trajectory and Alice's transmit power separately. Our examination shows that the GM method can significantly outperform the CI method in terms of achieving a higher average covert rate and the complexity of the GM method is lower than that of the CI method.