We consider the problem of a drone having to traverse a terrain. Traversal of the terrain exposes the drone to certain risks, e.g., concentration of chemicals, severe thunderstorm wind gusts or any disturbing weather phenomenon. The goal of the drone is to navigate the terrain while minimizing the amount of risk. We develop a framework for quantifying the exposure to risk factors in a circular zone model. We propose risky zone avoidance navigation strategies for rectilinear or curvilinear drone trajectories. We validate the work using numeric simulations.