Problem-solving is an essential part of teaching, learning, and assessment of physics and mathematics. The continuing educational reforms have a deep impact on everyday teaching as well as working with talented students. In the Macedonian educational system, the curricula do not explicitly point out the connection between mathematics and physics, but findings show that if the students do not understand the connection, they have problems adopting the knowledge. The gap that appears in applying geometry subsists even among talented students. When solving problems of geometrical optics, besides physics, it is inevitable that students use the standard geometrical apparatus. Even when the basics of physics are well known, possible mathematical mistakes often lead to wrong results in the given problems in physics. Here we demonstrate such an example of a selected problem from Macedonian state competitions in physics. The case study investigates two samples of students, 18 primary school students and 67 high school students, involved in State physics competitions in the year 2016. The selected problems have similar demands.