This article adapts the problem-solving model developed by Polya to investigate and give an innovative approach to discuss and solve an optimization problem in geometry: the Regiomontanus Problem and its application to football. Various mathematical tools, such as calculus, inequality and the properties of circles, are used to explore and reflect on the different aspects of the problem and its solution. In addition, other than the traditional calculus approach to solve this problem, an elegant geometric approach is introduced.