Geometric Algebra can be considered as a very useful language for dealing with mathematics, physics and computer science. Among the various algebras commonly used by practitioners of GA, Conformal Geometric Algebra (CGA) is of special interest for its powerful transformations and its ability to represent any hypersphere or hyperplane. Moreover, CGA is an algebra capable of representing pencils of hyperspheres. This paper presents an approach for constructing Voronoi diagrams by using pencils of CGA to build cell interfaces from centroid positions. Power, multiplicatively weighted Voronoi and multiplicatively weighted power diagrams are also supported by the presented method. This allows the use of circles as centroids to add control to the weights of the cells and to the curvatures of their borders.