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…”.

1. The power h of a point P with respect to a circle C of radius R and center O is defined as h = d² − R², where d is the distance from P to the center O of the circle.

Authors and Affiliations

1. Department of Mathematics, University of Athens, Athens, Greece

   Nikolaos Metaxas & Andromachi Karagiannidou

Corresponding author

Correspondence toNikolaos Metaxas.

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