Dependency cycles pose a significant challenge to software quality and maintainability. However, there is limited understanding of how practitioners resolve dependency cycles in real-world scenarios. This paper presents an empirical study investigating the recurring patterns employed by software developers to resolve dependency cycles between two classes in practice. We analyzed the data from 38 open-source projects across different domains and manually inspected hundreds of cycle untangling cases. Our findings reveal that developers tend to employ five recurring patterns to address dependency cycles. The chosen patterns are not only determined by dependency relations between cyclic classes, but also highly related to their design context, i.e., how cyclic classes depend on or are depended by their neighbor classes. Through this empirical study, we also discovered three common counterintuitive solutions developers usually adopted during cycles' handling. These recurring patterns and common counterintuitive solutions observed in dependency cycles' practice can serve as a taxonomy to improve developers' awareness and also be used as learning materials for students in software engineering and inexperienced developers. Our results also suggest that, in addition to considering the internal structure of dependency cycles, automatic tools need to consider the design context of cycles to provide better support for refactoring dependency cycles.