In this note, an approach combining dynamic geometry and automated deduction techniques is used to study the bisectors between points and curves. Usual teacher constructions for bisectors are discussed, showing that inherent limitations in dynamic geometry software impede their thorough study. We show that the interactive sketching of bisectors and an automatic treatment of the algebraic problem involved can give a reasonable knowledge about them. Since some cases are currently out of computational scope, despite the simplicity of the bisector problem, we sketch an alternative method for dealing with them. (Contains 9 figures.)