Equal bisectors at a vertex of a triangle

Abstract

Given a triangle ABC, we study the conditions that its vertices must satisfy in order for the internal and external bisectors corresponding to one of the vertices to be equal. We investigate whether there are triangles for which the bisectors at each vertex are equal and other related properties. Automatic Deduction techniques (such as those described in [1]), implemented with CoCoA [2] and the dynamic geometry system GDI ([3], [4]), are used. Moreover, an ad-hoc GeoGebra [5] package has been developed (c.f. [6]) to facilitate the exploration of the problem and to improve the analysis and representation of the results in graphical form. © 2011 Springer-Verlag.