Abstract
It is shown how a well-known task, also used in the „VIVA Mathеmatics with Computer“ and “Theme of the Month” online competitions, can become a base for regular classes and/or explorations in school STEM centers. The task is related to a special case of the classical Holditch theorem and allows the development of various substantive studies using the GeoGebra system. The structure of the necessary GeoGebra auxiliary files for these studies is described. The analysis of the results of the participants in the mentioned competitions gives a reason to consider that the tasks in the article are accessible to students from upper secondary education. In addition to work in STEM centers, the article can be used in preparation for participation in the "VIVA Mathematics with a Computer" competition, as well as for developing skills for working on independent student research. The article would also be useful in the preparation of future teachers.
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