On strict strong constructibility with a compass alone
Let S be a set of points in the Euclidean plane. The authors show that every point of the plane which can be constructed by a compass and a ruler can be constructed as well by a compass alone subject to the following restriction: Choose two points 0 and K of S. Then every point is obtained as the proper intersection (no tangent points!) of two circles which are either symmetrical to the line OK or have their centres on OK. This improves an earlier paper of the authors [J. Geom. 30, 28-35 (1987; Zbl 0627.51017)].
scientific article; zbMATH DE number 4171834