Visualization of mathematical relationships enables students to formulate conjectures as well as to search for mathematical arguments to support these conjectures. In this project students are asked to discover the sufficient and necessary condition so that two circles form the circumscribed and inscribed circle of a triangle and investigate how this condition effects the type of triangle in general and its perimeter in particular. Its open-ended form of the task is a departure from the usual phrasing of textbook’s exercises “show that…”.
Nikolaos Metaxas and Andromachi Karagiannidou have written an article called When Two Circles Determine a Triangle. Discovering and Proving a Geometrical Condition in a Computer Environment. This article was published online in the International Journal of Computers for Mathematical Learning on Sunday. Here is the abstract of their article: