Throughout the entire development period of mathematics, geometric constructions have been examined by renowned mathematicians, each of whom made his own contribution to the understanding of the possibilities of constructions. Over the years, other branches were added to geometric constructions, such as: construction using a straightedge only, construction using a compass only and construction using a graded ruler.
In the paper we present original, previously unknown tasks of finding the center of a circle by using a straightedge only. The tasks were given as part of a course in “geometric constructions” given to students in a post-primary route of teachers’ training in mathematics.
In each task we present a description of the construction based on an investigation carried out by the pre-service teachers using dynamic software (Geogebra) so as to bring the students to use computer tools, and to harness the capabilities of these tools to improve the teaching and learning processes. The surprising aspect of the tasks is that although only the use of the straightedge was allowed, they can still be accomplished.