Generative artificial intelligence (GenAI) and large language models (LLMs) offer new opportunities for teachers to create digital learning resources. However, limited research has examined how educators use prompting strategies to develop instructional tools in classroom contexts. This study employed an embedded single-case study design to investigate how fifteen in-service secondary mathematics teachers in Hong Kong developed Artificial Intelligence-Technological Pedagogical Content Knowledge (AI-TPACK) through participation in a professional learning network. The professional learning circle served as the primary case, with three embedded units of analysis examining the development of a Socratic tutor applet, a three-dimensional disc-method visualization tool, and an automated calculus worksheet generator. Findings indicate that teachers engaged in an iterative design process in which curriculum goals were translated into prompts and subsequently refined to produce digital learning resources. Collaborative problem-solving within the learning community helped teachers address practical challenges, including maintaining output quality across multiple interactions and ensuring the accurate presentation of mathematical notation and representations. The findings highlight the importance of AI-technological knowledge (AI-TK) in supporting teachers' effective use of AI tools and provide insights into how AI can be integrated into the design of teaching and learning resources in secondary mathematics and STEM education.