Sobre a existência e construção de um triângulo dadas suas bissetrizes internas

Abstract

The present paper consists of presenting results regarding the following questions: given three positive numbers arbitrary n, o, q, is there a triangle with internal bisectors of length n, o, q? Is it possible to construct such a triangle with ruler and compass? This dissertation is the result of a bibliographical research where we raise the history of the problems in focus, and present the necessary theory for the demonstrations. In the first chapter we introduce the problems, commenting a little on their history. We continue in the second chapter, presenting the necessary preliminaries for the development of the demonstrations of the problems. In the sequence we present the intended demonstrations, and finally we conclude the text with our considerations, where we highlight the recognize the importance of the existing interrelations between elements of different areas of Mathematics.