Problema de Apolônio: uma abordagem algébrica com auxílio do computador.

Abstract

Tangency problems involving points, lines and circles in the plane, such as the famous Problem of Apollonius, can be formulated and solved, in a conceptually simple way, using nothing more than high school algebra. However, the necessary calculations can be laborious and prone to error, making the algebraic approach less attractive. In this work, we will investigate how the algebra of cycles and a computational algebra system (the GeoGebra CAS Window) can be used to help us solve these problems. We will also see how GeoGebra’s visualization capabilities can be used to better understand the relationship between algebra and geometry