Nowe cechy równoboczności trójkątów

Abstract

In this paper the authors formulate and prove several conditions for triangle to be equilateral. These conditions are associated with Gergonne, Nagel and Torricelli points and were obtained by composing and solving the so-called ‘enforcement tasks’. Both, the method and the results, can be used to trigger some mathematical student activities at different levels of education or even some teacher activities.