EJMT Abstract

In geometrical constructions using a straightedge only the drawing of a tangent to a given circle without indication of the location of its center is a basic construction for solving many problems in this field. The correctness of this construction is usually based on concepts from Projective and Synthetic Geometry (polar, harmonic range etc.) which is not widely known among the undergraduate students and even among the teachers. In the article we give two elementary proofs of the correctness of such a construction: the first using analytical geometry and trigonometry and the second using the Euclidean geometry only. In addition, we shall discuss the advantages of using dynamic software for illustrating the construction of tangents.